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Journal articles on the topic 'Algebraic geometric codes'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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1

Chen, Hao. "Testing algebraic geometric codes." Science in China Series A: Mathematics 52, no. 10 (August 8, 2009): 2171–76. http://dx.doi.org/10.1007/s11425-009-0141-4.

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2

Chen, H., S. Ling, and C. Xing. "Quantum Codes From Concatenated Algebraic-Geometric Codes." IEEE Transactions on Information Theory 51, no. 8 (August 2005): 2915–20. http://dx.doi.org/10.1109/tit.2005.851760.

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3

Walker, Judy L. "Algebraic geometric codes over rings." Journal of Pure and Applied Algebra 144, no. 1 (December 1999): 91–110. http://dx.doi.org/10.1016/s0022-4049(98)00047-4.

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4

Lint, J. H. van. "Book Review: Algebraic-geometric codes." Bulletin of the American Mathematical Society 27, no. 2 (October 1, 1992): 306–11. http://dx.doi.org/10.1090/s0273-0979-1992-00311-7.

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5

Chen, Hao. "Algebraic geometric codes with applications." Frontiers of Mathematics in China 2, no. 1 (March 2007): 1–11. http://dx.doi.org/10.1007/s11464-007-0001-x.

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6

Sorensen, A. B. "Weighted Reed-Muller codes and algebraic-geometric codes." IEEE Transactions on Information Theory 38, no. 6 (1992): 1821–26. http://dx.doi.org/10.1109/18.165459.

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7

Shokrollahi, M. A., and H. Wasserman. "List decoding of algebraic-geometric codes." IEEE Transactions on Information Theory 45, no. 2 (March 1999): 432–37. http://dx.doi.org/10.1109/18.748993.

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8

Pellikan, R., B. Z. Shen, and G. J. M. van Wee. "Which linear codes are algebraic-geometric?" IEEE Transactions on Information Theory 37, no. 3 (May 1991): 583–602. http://dx.doi.org/10.1109/18.79915.

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9

Davis, Jennifer A. "Algebraic geometric codes on anticanonical surfaces." Journal of Pure and Applied Algebra 215, no. 4 (April 2011): 496–510. http://dx.doi.org/10.1016/j.jpaa.2010.06.002.

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10

Duursma, Iwan, Radoslav Kirov, and Seungkook Park. "Distance bounds for algebraic geometric codes." Journal of Pure and Applied Algebra 215, no. 8 (August 2011): 1863–78. http://dx.doi.org/10.1016/j.jpaa.2010.10.018.

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11

Maharaj, H. "Explicit Constructions of Algebraic-Geometric Codes." IEEE Transactions on Information Theory 51, no. 2 (February 2005): 714–22. http://dx.doi.org/10.1109/tit.2004.840896.

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12

Duursma, Iwan M., and Seungkook Park. "Coset bounds for algebraic geometric codes." Finite Fields and Their Applications 16, no. 1 (January 2010): 36–55. http://dx.doi.org/10.1016/j.ffa.2009.11.006.

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13

Tsfasman, Michael A. "Algebraic-geometric codes and asymptotic problems." Discrete Applied Mathematics 33, no. 1-3 (November 1991): 241–56. http://dx.doi.org/10.1016/0166-218x(91)90120-l.

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14

Leonard, D. A. "Error-locator ideals for algebraic-geometric codes." IEEE Transactions on Information Theory 41, no. 3 (May 1995): 819–24. http://dx.doi.org/10.1109/18.382034.

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15

Hoholdt, T., and R. Pellikaan. "On the decoding of algebraic-geometric codes." IEEE Transactions on Information Theory 41, no. 6 (1995): 1589–614. http://dx.doi.org/10.1109/18.476214.

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16

Skorobogatov, A. N., and S. G. Vladut. "On the decoding of algebraic-geometric codes." IEEE Transactions on Information Theory 36, no. 5 (1990): 1051–60. http://dx.doi.org/10.1109/18.57204.

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17

Calderini, Marco, and Giorgio Faina. "Generalized Algebraic Geometric Codes From Maximal Curves." IEEE Transactions on Information Theory 58, no. 4 (April 2012): 2386–96. http://dx.doi.org/10.1109/tit.2011.2177068.

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18

Miura, Shinji. "Algebraic geometric codes on certain plane curves." Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 76, no. 12 (1993): 1–13. http://dx.doi.org/10.1002/ecjc.4430761201.

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19

Chen, L., R. A. Carrasco, and M. Johnston. "List decoding performance of algebraic geometric codes." Electronics Letters 42, no. 17 (2006): 986. http://dx.doi.org/10.1049/el:20061999.

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20

Nardi, Jade. "Algebraic geometric codes on minimal Hirzebruch surfaces." Journal of Algebra 535 (October 2019): 556–97. http://dx.doi.org/10.1016/j.jalgebra.2019.06.022.

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21

Hao Chen. "Some good quantum error-correcting codes from algebraic-geometric codes." IEEE Transactions on Information Theory 47, no. 5 (July 2001): 2059–61. http://dx.doi.org/10.1109/18.930942.

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22

Deundyak, Vladimir M., and Denis V. Zagumennov. "On the Properties of Algebraic Geometric Codes as Copy Protection Codes." Modeling and Analysis of Information Systems 27, no. 1 (March 23, 2020): 22–38. http://dx.doi.org/10.18255/1818-1015-2020-1-22-38.

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Traceability schemes which are applied to the broadcast encryption can prevent unauthorized parties from accessing the distributed data. In a traceability scheme a distributor broadcasts the encrypted data and gives each authorized user unique key and identifying word from selected error-correcting code for decrypting. The following attack is possible in these schemes: groups of c malicious users are joining into coalitions and gaining illegal access to the data by combining their keys and identifying codewords to obtain pirate key and codeword. To prevent this attacks, classes of error-correcting codes with special c-FP and c-TA properties are used. In particular, c -FP codes are codes that make direct compromise of scrupulous users impossible and c -TA codes are codes that make it possible to identify one of the a‹ackers. We are considering the problem of evaluating the lower and the upper boundaries on c, within which the L-construction algebraic geometric codes have the corresponding properties. In the case of codes on an arbitrary curve the lower bound for the c-TA property was obtained earlier; in this paper, the lower bound for the c-FP property was constructed. In the case of curves with one infinite point, the upper bounds for the value of c are obtained for both c-FP and c-TA properties. During our work, we have proved an auxiliary lemma and the proof contains an explicit way to build a coalition and a pirate identifying vector. Methods and principles presented in the lemma can be important for analyzing broadcast encryption schemes robustness. Also, the c-FP and c-TA boundaries monotonicity by subcodes are proved.
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23

Le, Phong, and Sunil Chetty. "On the Dimension of Algebraic-Geometric Trace Codes." Mathematics 4, no. 2 (May 7, 2016): 32. http://dx.doi.org/10.3390/math4020032.

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24

Fernandez, M., and M. Soriano. "Identification of Traitors in Algebraic-Geometric Traceability Codes." IEEE Transactions on Signal Processing 52, no. 10 (October 2004): 3073–77. http://dx.doi.org/10.1109/tsp.2004.833858.

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25

Leonard, D. A. "A generalized Forney formula for algebraic-geometric codes." IEEE Transactions on Information Theory 42, no. 4 (July 1996): 1263–68. http://dx.doi.org/10.1109/18.508855.

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26

MAHARAJ, HIREN. "SPACES OF MODULAR FORMS AND ALGEBRAIC GEOMETRIC CODES." International Journal of Number Theory 08, no. 06 (August 3, 2012): 1485–502. http://dx.doi.org/10.1142/s1793042112500881.

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For ℓ = 2, 3, 5, we show that spaces of modular forms M2k(Γ0(ℓn)) are closely related to a class of one-point codes from the reduction of the modular tower {X0(ℓn)}n≥2 (mod p) for primes p > ℓ. Code construction from the space of cusp form is also considered.
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27

Johnston, M., R. A. Carrasco, and B. L. Burrows. "Design of algebraic-geometric codes over fading channels." Electronics Letters 40, no. 21 (2004): 1355. http://dx.doi.org/10.1049/el:20045392.

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28

Beelen, Peter. "The order bound for general algebraic geometric codes." Finite Fields and Their Applications 13, no. 3 (July 2007): 665–80. http://dx.doi.org/10.1016/j.ffa.2006.09.006.

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29

Park, Seungkook. "Coherence of sensing matrices coming from algebraic-geometric codes." Advances in Mathematics of Communications 10, no. 2 (April 2016): 429–36. http://dx.doi.org/10.3934/amc.2016016.

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30

Tapia1, H., and C. Rentería. "Some geometric-algebraic codes on a covering plane curve." Communications in Algebra 22, no. 15 (January 1994): 6401–8. http://dx.doi.org/10.1080/00927879408825196.

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31

Bartoli, D., L. Quoos, and G. Zini. "Algebraic geometric codes on many points from Kummer extensions." Finite Fields and Their Applications 52 (July 2018): 319–35. http://dx.doi.org/10.1016/j.ffa.2018.04.008.

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32

Anderson, Sarah E., and Gretchen L. Matthews. "Exponents of polar codes using algebraic geometric code kernels." Designs, Codes and Cryptography 73, no. 2 (June 25, 2014): 699–717. http://dx.doi.org/10.1007/s10623-014-9987-8.

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33

Besana, Alberto, and Cristina Martínez. "A Topological View of Reed–Solomon Codes." Mathematics 9, no. 5 (March 9, 2021): 578. http://dx.doi.org/10.3390/math9050578.

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We studied a particular class of well known error-correcting codes known as Reed–Solomon codes. We constructed RS codes as algebraic-geometric codes from the normal rational curve. This approach allowed us to study some algebraic representations of RS codes through the study of the general linear group GL(n,q). We characterized the coefficients that appear in the decompostion of an irreducible representation of the special linear group in terms of Gromov–Witten invariants of the Hilbert scheme of points in the plane. In addition, we classified all the algebraic codes defined over the normal rational curve, thereby providing an algorithm to compute a set of generators of the ideal associated with any algebraic code constructed on the rational normal curve (NRC) over an extension Fqn of Fq.
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34

Kuznetsov, A. A., I. P. Kolovanova, D. I. Prokopovych-Tkachenko, and T. Y. Kuznetsova. "ANALYSIS AND STUDYING OF THE PROPERTIES OF ALGEBRAIC GEOMETRIC CODES." Telecommunications and Radio Engineering 78, no. 5 (2019): 393–417. http://dx.doi.org/10.1615/telecomradeng.v78.i5.30.

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35

Feng, G. L., and T. R. N. Rao. "Decoding algebraic-geometric codes up to the designed minimum distance." IEEE Transactions on Information Theory 39, no. 1 (1993): 37–45. http://dx.doi.org/10.1109/18.179340.

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36

Ehrhard, D. "Achieving the designed error capacity in decoding algebraic-geometric codes." IEEE Transactions on Information Theory 39, no. 3 (May 1993): 743–51. http://dx.doi.org/10.1109/18.256485.

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37

Geil, Olav, Stefano Martin, Ryutaroh Matsumoto, Diego Ruano, and Yuan Luo. "Relative Generalized Hamming Weights of One-Point Algebraic Geometric Codes." IEEE Transactions on Information Theory 60, no. 10 (October 2014): 5938–49. http://dx.doi.org/10.1109/tit.2014.2345375.

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38

Wolper, James S. "Algebraic-Geometric Codes (M. A. Tsfasman and S. G. Vladui)." SIAM Review 35, no. 3 (September 1993): 541–43. http://dx.doi.org/10.1137/1035131.

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39

Chen, L., and R. A. Carrasco. "Soft decoding of algebraic–geometric codes using Koetter-Vardy algorithm." Electronics Letters 45, no. 25 (2009): 1334. http://dx.doi.org/10.1049/el.2009.0940.

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40

Guruswami, Venkatesan, and Anindya C. Patthak. "Correlated algebraic-geometric codes: Improved list decoding over bounded alphabets." Mathematics of Computation 77, no. 261 (January 1, 2008): 447–73. http://dx.doi.org/10.1090/s0025-5718-07-02012-1.

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41

Jian, Ren, and Xiao Guozhen. "On the decoding of algebraic geometric codes based on FIA." Journal of Electronics (China) 13, no. 1 (January 1996): 23–30. http://dx.doi.org/10.1007/bf02684711.

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42

Couvreur, Alain. "The dual minimum distance of arbitrary-dimensional algebraic–geometric codes." Journal of Algebra 350, no. 1 (January 2012): 84–107. http://dx.doi.org/10.1016/j.jalgebra.2011.09.030.

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43

Ba-Zhong Shen and K. K. Tzeng. "A code decomposition approach for decoding cyclic and algebraic-geometric codes." IEEE Transactions on Information Theory 41, no. 6 (1995): 1969–87. http://dx.doi.org/10.1109/18.476320.

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44

Chen, Hao, Hing Sun Luk, and Stephen Yau. "Explicit Computation of Generalized Hamming Weights for Some Algebraic Geometric Codes." Advances in Applied Mathematics 21, no. 1 (July 1998): 124–45. http://dx.doi.org/10.1006/aama.1998.0591.

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45

Skorobogatov, Alexei N. "The parameters of subcodes of algebraic-geometric codes over prime subfields." Discrete Applied Mathematics 33, no. 1-3 (November 1991): 205–14. http://dx.doi.org/10.1016/0166-218x(91)90116-e.

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46

Mita, S., and H. Matsui. "An effective error correction using a combination of algebraic geometric codes and Parity codes for HDD." IEEE Transactions on Magnetics 41, no. 10 (October 2005): 2992–94. http://dx.doi.org/10.1109/tmag.2005.854451.

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47

Johnston, M., and R. A. Carrasco. "Construction and performance of algebraic–geometric codes over AWGN and fading channels." IEE Proceedings - Communications 152, no. 5 (2005): 713. http://dx.doi.org/10.1049/ip-com:20045153.

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48

Gui-Liang Feng, V. K. Wei, T. R. N. Rao, and K. K. Tzeng. "Simplified understanding and efficient decoding of a class of algebraic-geometric codes." IEEE Transactions on Information Theory 40, no. 4 (July 1994): 981–1002. http://dx.doi.org/10.1109/18.335973.

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49

Sakata, S., J. Justesen, Y. Madelung, H. E. Jensen, and T. Hoholdt. "Fast decoding of algebraic-geometric codes up to the designed minimum distance." IEEE Transactions on Information Theory 41, no. 6 (1995): 1672–77. http://dx.doi.org/10.1109/18.476240.

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50

Park, Seungkook. "Floor type bound for the minimum distance of generalized algebraic geometric codes." Journal of Pure and Applied Algebra 220, no. 1 (January 2016): 175–79. http://dx.doi.org/10.1016/j.jpaa.2015.06.004.

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