Journal articles: 'M CODES'

1

Job, V. R. "m-adic residue codes." IEEE Transactions on Information Theory 38, no. 2 (March 1992): 496–501. http://dx.doi.org/10.1109/18.119710.

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2

Tallini, L. G., and U. Vaccaro. "Efficient m-ary balanced codes." Discrete Applied Mathematics 92, no. 1 (March 1999): 17–56. http://dx.doi.org/10.1016/s0166-218x(98)00129-2.

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3

Mahmoodi, Hamidreza. "Cyclic codes over R3,m." Discrete Mathematics, Algorithms and Applications 11, no. 01 (February 2019): 1950009. http://dx.doi.org/10.1142/s1793830919500095.

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Let [Formula: see text] be the ring [Formula: see text]. We study cyclic codes of arbitrary length [Formula: see text] over the ring [Formula: see text] and obtain a complete characterization for them by presenting a unique set of generators for these codes. For example, we try to determine all distinct cyclic codes of length [Formula: see text] over the ring [Formula: see text] by a practical algorithm.

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4

Wongroekdee, Sawitree, Kosin Chaiprathum, Virasit Imtawil, and Puripong Suthisopapan. "LDPC Coded 2^m-ary QAM for Ultra High Speed Communications." Applied Mechanics and Materials 781 (August 2015): 45–48. http://dx.doi.org/10.4028/www.scientific.net/amm.781.45.

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Modern communication systems that employ LDPC codes and QAM modulation can achieve high speed and reliable transmission without bandwidth expansion. In this paper, the performances of LDPC codes with 2m- ary QAM at m>10, which can provide enormous bandwidth efficiency, are studied. Bit error rate performances of various combinations of LDPC codes and order of QAM are provided. From the results, the performance of LDPC coded ultra-high order QAM is excellent making this system very attractive for ultra-high speed communications.

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5

Thangaraj, A., and S. W. McLaughlin. "Quantum codes from cyclic codes over GF(4/sup m/)." IEEE Transactions on Information Theory 47, no. 3 (March 2001): 1176–78. http://dx.doi.org/10.1109/18.915675.

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6

Ching-Nung Yang and Chi-Sung Laih. "DC/sub m/ codes for constructing t-EC/AUED codes." IEEE Transactions on Computers 47, no. 4 (April 1998): 492–95. http://dx.doi.org/10.1109/12.675719.

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7

Brualdi, Richard A., and Vera S. Pless. "Greedy codes." Journal of Combinatorial Theory, Series A 64, no. 1 (September 1993): 10–30. http://dx.doi.org/10.1016/0097-3165(93)90085-m.

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8

Tang, Yongsheng, Shixin Zhu, and Liqi Wang. "On Abelian codes over $${\mathbb {Z}}_{m}$$ Z m." Journal of Applied Mathematics and Computing 50, no. 1-2 (February 3, 2015): 259–73. http://dx.doi.org/10.1007/s12190-015-0869-7.

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9

Lei, Guo Wei, Yuan An Liu, and Xue Fang Xiao. "Threaded Space Time Code Design for CPM with Joint Decoding." Applied Mechanics and Materials 631-632 (September 2014): 847–50. http://dx.doi.org/10.4028/www.scientific.net/amm.631-632.847.

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In the letter, a system of continuous phase modulation (CPM) with threaded space time codes (TSTC) is proposed for multiple-input multiple-output systems. In the system, source bits are coded via outer coder of Reed Solomon (RS). The codeword of which is suitable for TSTC design. Then inner coder mainly converts binary symbols into M-ary symbols for purpose of CPM. At receiver, Joint soft decoding approach is considered. Finally simulation results are provided for VBLAST, DBLAST, and TSTC as comparison.

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10

Sayegh, S., and F. Hemmati. "Differentially encoded M-PSK block codes." IEEE Transactions on Communications 43, no. 9 (1995): 2426–28. http://dx.doi.org/10.1109/26.412715.

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11

Jain, Sapna. "Bursts in m-metric array codes." Linear Algebra and its Applications 418, no. 1 (October 2006): 130–41. http://dx.doi.org/10.1016/j.laa.2006.01.022.

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12

Pruthi, Manju. "Cyclic codes of length 2 m." Proceedings Mathematical Sciences 111, no. 4 (November 2001): 371–79. http://dx.doi.org/10.1007/bf02829612.

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13

Douillard, C., and C. Berrou. "Turbo Codes With Rate-<tex>$m/(m+ 1)$</tex>Constituent Convolutional Codes." IEEE Transactions on Communications 53, no. 10 (October 2005): 1630–38. http://dx.doi.org/10.1109/tcomm.2005.857165.

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14

TANG, Yongsheng, Ting YAO, Shixin ZHU, and Xiaoshan KAI. "A Family of Constacyclic Codes over 𝔽2 m + u𝔽2 m and Its Application to Quantum Codes." Chinese Journal of Electronics 29, no. 1 (January 1, 2020): 114–21. http://dx.doi.org/10.1049/cje.2019.10.007.

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15

Pelusi, Danilo, Samir Elmougy, Luca G. Tallini, and Bella Bose. "$m$ -ary Balanced Codes With Parallel Decoding." IEEE Transactions on Information Theory 61, no. 6 (June 2015): 3251–64. http://dx.doi.org/10.1109/tit.2015.2429139.

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16

McCarty, Janet. "Can ASHA Members Use E/M Codes?" ASHA Leader 13, no. 9 (July 2008): 3–18. http://dx.doi.org/10.1044/leader.bml.13092008.3.

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17

SUZUKI, K. "Complex M-Spotty Byte Error Control Codes." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E89-A, no. 9 (September 1, 2006): 2396–404. http://dx.doi.org/10.1093/ietfec/e89-a.9.2396.

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18

Yen, W. F. "(M – 1) and (M – 2) selfsynchronising M-ary codes generated with coding efficiency." IEE Proceedings - Communications 145, no. 2 (1998): 65. http://dx.doi.org/10.1049/ip-com:19981710.

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19

Yen, Chih-Ta, Ing-Jr Ding, and Cheng-Mu Tsai. "PERFORMANCE ANALYSIS OF SEVERAL QUASI-ORTHOGONAL CODES OPTICAL CDMA FOR RADIO-OVER-FIBER SYSTEM." Transactions of the Canadian Society for Mechanical Engineering 37, no. 3 (September 2013): 415–26. http://dx.doi.org/10.1139/tcsme-2013-0031.

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An optical code-division multiple-access (OCDMA) network for radio-over-fiber (RoF) transmissions was proposed. The network encoders/decoders (codecs) were structured based on arrayed-waveguide-grating (AWG) routers coded using modified prime codes (MPCs). In the proposed system, the lower in-phase cross correlation could reduce the beating noise, and in the proposed study, its performance was compared with that of a conventional system that uses M-sequence and Walsh-Hadamard codes. The performance of both systems was numerically evaluated by analyzing the effect of phase-induced-intensity noise (PIIN). The results showed that the new code families that had lower cross correlation can suppress the intensity of the noise and effectively cancel out the multiple-access interference (MAI) in balanced detection processes, which improved system performance. By using the proposed MPC-coded OCDMA ROF network codecs, each network required only two AWG routers to accomplish the spectral coding of radio base stations (RBSs) and the decoding of control stations (CSs), resulting in a simple and low-cost system. Therefore, it is possible to produce interference- and crosstalk-free optical CDMA systems for RoF transmissions.

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20

Leslie, Martin. "Hypermap-homology quantum codes." International Journal of Quantum Information 12, no. 01 (February 2014): 1430001. http://dx.doi.org/10.1142/s0219749914300010.

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We introduce a new type of sparse CSS quantum error correcting code based on the homology of hypermaps. Sparse quantum error correcting codes are of interest in the building of quantum computers due to their ease of implementation and the possibility of developing fast decoders for them. Codes based on the homology of embeddings of graphs, such as Kitaev's toric code, have been discussed widely in the literature and our class of codes generalize these. We use embedded hypergraphs, which are a generalization of graphs that can have edges connected to more than two vertices. We develop theorems and examples of our hypermap-homology codes, especially in the case that we choose a special type of basis in our homology chain complex. In particular the most straightforward generalization of the m × m toric code to hypermap-homology codes gives us a [(3/2)m2, 2, m] code as compared to the toric code which is a [2m2, 2, m] code. Thus we can protect the same amount of quantum information, with the same error-correcting capability, using less physical qubits.

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21

Yen, W. F. "Algorithm for creating (M−1) selfsynchronising M-ary variable length codes." Electronics Letters 27, no. 9 (1991): 740. http://dx.doi.org/10.1049/el:19910460.

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22

Güzeltepe, Murat, and Mustafa Eröz. "Quantum codes from codes over the ring $\mathbb{F}_{2^m}+\alpha \mathbb{F}_{2^m}+\beta \mathbb{F}_{2^m}+ \gamma \mathbb{F}_{2^m}$." Journal of Universal Mathematics 2, no. 2 (July 29, 2019): 127–36. http://dx.doi.org/10.33773/jum.590694.

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23

Baldi, Marco, Giovanni Cancellieri, Franco Chiaraluce, and Amedeo De Amicis De Amicis. "Regular and Irregular Multiple Serially- Concatenated Multiple-Parity-Check Codes for Wireless Applications." Journal of Communications Software and Systems 5, no. 4 (December 20, 2009): 140. http://dx.doi.org/10.24138/jcomss.v5i4.200.

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Multiple Serially-Concatenated Multiple-Parity-Check (M-SC-MPC) codes are a class of structured Low-Density Parity-Check (LDPC) codes, characterized by very simple encoding, that we have recently introduced. This paper evidences how the design of M-SC-MPC codes can be optimized for their usage in wireless applications. For such purpose, we consider some Quasi-Cyclic LDPC codes included in the mobile WiMax standard, and compare their performance with that of M-SCMPC codes having the same parameters. We also present a simple modification of the inner structure of M-SC-MPC codes that can help to improve their error correction performance by introducing irregularity in the parity-check matrix and increasing the length of local cycles in the associated Tanner graph. Our results show that regular and irregular M-SC-MPC codes, so obtained, can achieve very good performance and compare favorably with standard codes.

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24

Rani, Saroj. "On Cyclic and Negacyclic Codes of Length 8p^s Over Fp^m + uFp^m." Journal of the Indian Mathematical Society 87, no. 3-4 (July 1, 2020): 231. http://dx.doi.org/10.18311/jims/2020/23906.

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In this paper, we establish the algebraic structure of all cyclic and negacyclic codes of length 8ps over the chain ring Fpm + uFpm in terms of their generator polynomials, where u2 = 0 and s is a positive integer and p is an odd prime. We also find out the number of codewords in each of these cyclic codes. Besides this, we determine duals of cyclic codes and list self-dual cyclic and negacyclic codes of length 8ps over Fpm + uFpm. Also, we determine μ and -constacyclic codes of length 8ps over Fpm + uFpm.

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25

RÚA, IGNACIO F. "NONBINARY DELSARTE–GOETHALS CODES AND FINITE SEMIFIELDS." Glasgow Mathematical Journal 62, S1 (May 7, 2020): S186—S205. http://dx.doi.org/10.1017/s0017089520000191.

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AbstractSymplectic finite semifields can be used to construct nonlinear binary codes of Kerdock type (i.e., with the same parameters of the Kerdock codes, a subclass of Delsarte–Goethals codes). In this paper, we introduce nonbinary Delsarte–Goethals codes of parameters $(q^{m+1}\ ,\ q^{m(r+2)+2}\ ,\ {\frac{q-1}{q}(q^{m+1}-q^{\frac{m+1}{2}+r})})$ over a Galois field of order $q=2^l$ , for all $0\le r\le\frac{m-1}{2}$ , with m ≥ 3 odd, and show the connection of this construction to finite semifields.

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26

Kassim, Noordiana, Yusri Yusof, Nazri Mohd Nawi, and Mohd Zakiyamani Awang. "The Development of New STEP-NС Code Generator (Milling STEP Coder)." Applied Mechanics and Materials 465-466 (December 2013): 667–71. http://dx.doi.org/10.4028/www.scientific.net/amm.465-466.667.

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This research explored ISO 14649 together with ISO 6983 and utilize STEP-NC in overcoming the problems of G & M code and at the same time take advantage of the current advances in computing and controllers. A new STEP-NC Code Generator called Milling STEP Coder, which focuses on the milling process that are able to generate STEP-NC codes based on ISO 14649 Part 11 was developed. This system also has the capabilities to visualize the STEP-NC codes generated in a parent to child relationship tree-view structure, as well as give an image visualization of how the end machining will appears. The developed Milling STEP Coder uses Software Prototyping Model as its software development methodology, instead of the normal waterfall model, as prototype is a valuable mechanism for gaining better understanding of the system requirements. A small-scale mock up of the system was developed following an iterative modification process. The advantages of the proposed Milling STEP Coder program was verified and evaluated. The Milling STEP Coder can generates STEP-NC codes through a STEP-NC compliant interface and will give industries and academician more in-depth understanding and confidence to make the switch from G & M code to STEP-NC.

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27

Gao, You, and Gang Wang. "Bounds on Subspace Codes Based on Subspaces of Type(m,1)in Singular Linear Space." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/497958.

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The Sphere-packing bound, Singleton bound, Wang-Xing-Safavi-Naini bound, Johnson bound, and Gilbert-Varshamov bound on the subspace codesn+l,M,d,(m,1)qbased on subspaces of type(m,1)in singular linear spaceFq(n+l)over finite fieldsFqare presented. Then, we prove that codes based on subspaces of type(m,1)in singular linear space attain the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures inFq(n+l).

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28

Efanov, Dmitry, Valery Sapozhnikov, and Vladimir Sapozhnikov. "Two-Module Weight-Based Sum Code in Residue Ring Modulo M=4." SPIIRAS Proceedings 19, no. 3 (June 1, 2020): 674–713. http://dx.doi.org/10.15622/sp.2020.19.3.8.

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The paper describes research results of features of error detection in data vectors by sum codes. The task is relevant in this setting, first of all, for the use of sum codes in the implementation of the checkable discrete systems and the technical means for the diagnosis of their components. Methods for sum codes constructing are described. A brief overview in the field of methods for sum codes constructing is provided. The article highlights codes for which the values of all data bits are taken into account once by the operations of summing their values or the values of the weight coefficients of the bits during the formation of the check vector. The paper also highlights codes that are formed when the data vectors are initially divided into subsets, in particular, into two subsets. An extension of the sum code class obtained by isolating two independent parts in the data vectors, as well as weighting the bits of the data vectors at the stage of code construction, is proposed. The paper provides a generalized algorithm for two-module weighted codes construction, and describes their features obtained by weighing with non-ones weight coefficients for one of data bits in each of the subvectors, according to which the total weight is calculated. Particular attention is paid to the two-module weight-based sum code, for which the total weight of the data vector in the residue ring modulo M = 4 is determined. It is shown that the purpose of the inequality between the bits of the data vector in some cases gives improvements in the error detection characteristics compared to the well-known two-module codes. Some modifications of the proposed two-module weighted codes are described. A method for calculating the total number of undetectable errors in the two-module sum codes in the residue ring modulo M = 4 with one weighted bit in each of the subsets is proposed. Detailed characteristics of error detection by the considered codes both by the multiplicities of undetectable errors and by their types (unidirectional, symmetrical and asymmetrical errors) are given. The proposed codes are compared with known codes. A method for the synthesis of two-module sum encoders on a standard element base of the single signals adders is proposed. The classification of two-module sum codes is presented.

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29

Furber, Steve B., W. John Bainbridge, J. Mike Cumpstey, and Steve Temple. "Sparse distributed memory using N-of-M codes." Neural Networks 17, no. 10 (December 2004): 1437–51. http://dx.doi.org/10.1016/j.neunet.2004.07.003.

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30

Szulakiewicz, P. "M-ary linear phase multi-T phase codes." IEEE Transactions on Communications 37, no. 3 (March 1989): 197–99. http://dx.doi.org/10.1109/26.20092.

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31

Leonardo, E. J., Lin Zhang, and B. S. Vucetic. "Multidimensional M-PSK trellis codes for fading channels." IEEE Transactions on Information Theory 42, no. 4 (July 1996): 1093–108. http://dx.doi.org/10.1109/18.508835.

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32

French, C., G. Dixon, and J. Wolf. "Results involving (D,K) constrained M-ary codes." IEEE Transactions on Magnetics 23, no. 5 (September 1987): 3678–80. http://dx.doi.org/10.1109/tmag.1987.1065196.

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33

Du, J., and B. Vucetic. "New M-PSK trellis codes for fading channels." Electronics Letters 26, no. 16 (1990): 1267. http://dx.doi.org/10.1049/el:19900816.

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34

Rajan, B. Sundar, and M. U. Siddiqi. "Transform domain characterization of cyclic codes overZ m." Applicable Algebra in Engineering, Communication and Computing 5, no. 5 (September 1994): 261–75. http://dx.doi.org/10.1007/bf01225641.

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35

Liu, Haiyan, K. P. Shum, and Yuqi Guo. "Some Results on $${(\varvec{k,m})}$$-Comma Codes." Bulletin of the Iranian Mathematical Society 46, no. 4 (December 9, 2019): 1143–62. http://dx.doi.org/10.1007/s41980-019-00318-z.

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36

Mohammed, Mohanad Ali, Ameer J. Munshid, and Mehdi Alaeiyan. "Cyclic codes of length pn over (ℤp)m." Journal of Discrete Mathematical Sciences and Cryptography 24, no. 2 (February 17, 2021): 579–88. http://dx.doi.org/10.1080/09720529.2021.1891693.

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37

Shah, Tariq, and Naveed Ahmed Azam. "Characterization of cyclic codes over {ℬ[X;(1/m)Z0]}m > 1and efficient encoding decoding algorithm for cyclic codes." International Journal of Computer Mathematics 94, no. 5 (March 30, 2016): 1015–27. http://dx.doi.org/10.1080/00207160.2016.1158815.

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38

Puppe, V. "Group Actions and Codes." Canadian Journal of Mathematics 53, no. 1 (February 1, 2001): 212–24. http://dx.doi.org/10.4153/cjm-2001-009-0.

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AbstractA 2-action with “maximal number of isolated fixed points” (i.e., with only isolated fixed points such that dimk(⊕iHi (M; k)) = |M2|, k = ) on a 3-dimensional, closed manifold determines a binary self-dual code of length = . In turn this code determines the cohomology algebra H*(M; k) and the equivariant cohomology . Hence, from results on binary self-dual codes one gets information about the cohomology type of 3-manifolds which admit involutions with maximal number of isolated fixed points. In particular, “most” cohomology types of closed 3-manifolds do not admit such involutions. Generalizations of the above result are possible in several directions, e.g., one gets that “most” cohomology types (over ) of closed 3-manifolds do not admit a non-trivial involution.

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39

Rushanan, Joseph J. "Duadic codes and difference sets." Journal of Combinatorial Theory, Series A 57, no. 2 (July 1991): 254–61. http://dx.doi.org/10.1016/0097-3165(91)90049-m.

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40

Bhattacharya, Prabir, and Azriel Rosenfeld. "Contour codes of isothetic polygons." Computer Vision, Graphics, and Image Processing 50, no. 3 (June 1990): 353–63. http://dx.doi.org/10.1016/0734-189x(90)90153-m.

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41

Crnković, Dean, Andrea Švob, and Vladimir D. Tonchev. "Cyclotomic Trace Codes." Algorithms 12, no. 8 (August 13, 2019): 168. http://dx.doi.org/10.3390/a12080168.

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A generalization of Ding’s construction is proposed that employs as a defining set the collection of the sth powers ( s ≥ 2 ) of all nonzero elements in G F ( p m ) , where p ≥ 2 is prime. Some of the resulting codes are optimal or near-optimal and include projective codes over G F ( 4 ) that give rise to optimal or near optimal quantum codes. In addition, the codes yield interesting combinatorial structures, such as strongly regular graphs and block designs.

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42

Lema, Gebrehiwet Gebrekrstos, Teklehaymanot Baweke Reda, Dawit Hailu, and Tole Sutikno. "Performance evaluation of space time trellis coded MIMO for mobile communications." Indonesian Journal of Electrical Engineering and Computer Science 15, no. 3 (September 1, 2019): 1501. http://dx.doi.org/10.11591/ijeecs.v15.i3.pp1501-1508.

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The major enemy of wireless communication is multipath fading that highly degrades the received signal. Spatial diversity highly reduces deep fades of the wireless communication. Higher signal to noise ratio (SNR) requirement can be reduced by using space time coding. In this paper, the error performance of un-coded MIMO, different diversity combing methods, space time block codes and space time trellis codes are analyzed using different parameters including number of antennas, M-array modulations, trace criteria, rank and determinant. The simulation results have shown that the Bit Error Rate (BER) significantly reduces with increasing number of receiver antennas. However, the number of antennas that a mobile device can have is limited by its size and this is inconvenient for mobile communication. Hence, this paper suggests space time codes to mitigate multipath problems in mobile communication. So, BER performance of space time block codes scheme was evaluated by varying the number of transmitter and receiver antennas along with varying M-array PSK modulation orders. The results have shown that better BER is possible by integrating space time codes with spatial diversity. Finally, the error performance of space time trellis codes was evaluated by using trace, rank and determinant, and the simulation results depicted that better error performance is achieved using the proposed multipath reduction method.

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43

Fitzpatrick, Patrick, and John A. Ryan. "Counting irreducible Goppa codes." Journal of the Australian Mathematical Society 71, no. 3 (December 2001): 299–306. http://dx.doi.org/10.1017/s1446788700002949.

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AbstractWe consider ineducible Goppa codes of length qm over Fq defined by polynomials of degree r, where q = pt and p, m, r are distinct primes. The number of such codes, inequivalent under coordinate permutations and field automorphisms, is determined.

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44

Markkanen, M., J. Vierinen, and J. Markkanen. "Polyphase alternating codes." Annales Geophysicae 26, no. 8 (August 5, 2008): 2237–43. http://dx.doi.org/10.5194/angeo-26-2237-2008.

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Abstract. We present a new class of alternating codes. Instead of the customary binary phase codes, the new codes utilize either p or p–1 phases, where p is a prime number. The first class of codes has code length pm, where m is a positive integer, the second class has code length p–1. We give an actual construction algorithm, and explain the principles behind it. We handle a few specific examples in detail. The new codes offer an enlarged collection of code lengths for radar experiments.

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45

Kunimochi, Yoshiyuki. "Some Properties of Extractable Codes and Insertable Codes." International Journal of Foundations of Computer Science 27, no. 03 (February 2016): 327–42. http://dx.doi.org/10.1142/s0129054116400128.

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This paper deals with insertability and mainly extractablity of codes. A code C is called insertable (or extractable) if the free submonoid C* generated by C satisfies if z, [Formula: see text] implies [Formula: see text] (or z, [Formula: see text] implies [Formula: see text]). We show that a finite insertable code is a full uniform code. On the other hand there are many finite extractable codes which are not full uniform codes. We cannot still characterize the structures of infinite extractable codes. Here we give some results on the class of infix extractable codes. First, we consider a necessary and sufficient condition whether a given infix code C is extractable or not by using the syntactic graph of the code. Secondly, we investigate the extractability for the families of other related bifix codes. We newly define the bifix codes, called e(m)-codes and [Formula: see text]-codes, and refer to the extractability of them.

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46

THAKRAN, SEEMA, and VINOD TYAGI. "NEW CLASS OF DOUBLE INDUCTIVE ERROR CORRECTING CODES BASED ON THE CLASS OF GRM AND DGRM CODES OVER GF(2)." Discrete Mathematics, Algorithms and Applications 06, no. 01 (February 18, 2014): 1450007. http://dx.doi.org/10.1142/s1793830914500074.

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In this paper, a new class of codes over GF(2) is introduced. The codes have length n = 3/2 ⋅ 2m(m ≥ 4), and have a similar 'double inductive' structure to that possessed by the class of GRM and DGRM codes. The new codes are constructed in a way such that their length-to-distance ratio n/d = 2m(m ≥ 3).

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47

Kieft, Johan, and Wolter Tjaarda. "Als je bij het invoeren van je codes eenmaal T-codes hebt gebruikt mag je daarna overgaan op M-codes?" Mondhygienisten vademecum 9, no. 4 (April 2011): 3–4. http://dx.doi.org/10.1007/s12465-011-0008-8.

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48

Ali, Mumtaz, Huma Khan, Le Son, Florentin Smarandache, and W. Kandasamy. "New Soft Set Based Class of Linear Algebraic Codes." Symmetry 10, no. 10 (October 16, 2018): 510. http://dx.doi.org/10.3390/sym10100510.

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In this paper, we design and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. The advantage of using these codes is that they have the ability to transmit m-distinct messages to m-set of receivers simultaneously. The methods of generating and decoding these new classes of soft linear algebraic codes have been developed. The notion of soft canonical generator matrix, soft canonical parity check matrix, and soft syndrome are defined to aid in construction and decoding of these codes. Error detection and correction of these codes are developed and illustrated by an example.

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49

Sharma, Anuradha, and Amit K. Sharma. "Construction of self-dual codes over ℤ 2 m $\mathbb {Z}_{2^{m}}$." Cryptography and Communications 8, no. 1 (January 2016): 83–101. http://dx.doi.org/10.1007/s12095-015-0139-4.

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Huang, Lei, and Shixin Zhu. "Constacyclic codes of arbitrary lengths over ring $$Z_{p^m } + vZ_{p^m }$$." Journal of Electronics (China) 31, no. 3 (June 2014): 222–26. http://dx.doi.org/10.1007/s11767-014-3167-x.

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Journal articles on the topic 'M CODES'

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