Academic literature on the topic 'Hamming codes'

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Journal articles on the topic "Hamming codes"

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Rifà, J., F. I. Solov’eva, and M. Villanueva. "Intersection of Hamming codes avoiding Hamming subcodes." Designs, Codes and Cryptography 62, no. 2 (2011): 209–23. http://dx.doi.org/10.1007/s10623-011-9506-0.

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Upadhyay, Rohitkumar R. "Hamming Codes: Error Reducing Techniques." International Journal for Research in Applied Science and Engineering Technology 9, no. 11 (2021): 1972–74. http://dx.doi.org/10.22214/ijraset.2021.39146.

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Abstract: Hamming codes for all intents and purposes are the first nontrivial family of error-correcting codes that can actually correct one error in a block of binary symbols, which literally is fairly significant. In this paper we definitely extend the notion of error correction to error-reduction and particularly present particularly several decoding methods with the particularly goal of improving the error-reducing capabilities of Hamming codes, which is quite significant. First, the error-reducing properties of Hamming codes with pretty standard decoding definitely are demonstrated and ex
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Barashko, A. S. "Polynomials generating Hamming codes." Ukrainian Mathematical Journal 45, no. 7 (1993): 987–92. http://dx.doi.org/10.1007/bf01057445.

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Bauer, Friedrich L. "Richard Hamming: Fehlerkorrigierende Codes." Informatik-Spektrum 30, no. 2 (2007): 95–99. http://dx.doi.org/10.1007/s00287-006-0135-3.

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Borges, Joaquim, Josep Rifà, and Victor Zinoviev. "Completely regular codes by concatenating Hamming codes." Advances in Mathematics of Communications 12, no. 2 (2018): 337–49. http://dx.doi.org/10.3934/amc.2018021.

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González-Sarabia, Manuel, Delio Jaramillo, and Rafael H. Villarreal. "On the generalized Hamming weights of certain Reed–Muller-type codes." Analele Universitatii "Ovidius" Constanta - Seria Matematica 28, no. 1 (2020): 205–17. http://dx.doi.org/10.2478/auom-2020-0014.

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AbstractThere is a nice combinatorial formula of P. Beelen and M. Datta for the r-th generalized Hamming weight of an a ne cartesian code. Using this combinatorial formula we give an easy to evaluate formula to compute the r-th generalized Hamming weight for a family of a ne cartesian codes. If 𝕏 is a set of projective points over a finite field we determine the basic parameters and the generalized Hamming weights of the Veronese type codes on 𝕏 and their dual codes in terms of the basic parameters and the generalized Hamming weights of the corresponding projective Reed–Muller-type codes on 𝕏
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Rifà, J., F. I. Solov’eva, and M. Villanueva. "Erratum to: Intersection of Hamming codes avoiding Hamming subcodes." Designs, Codes and Cryptography 74, no. 1 (2014): 283. http://dx.doi.org/10.1007/s10623-014-0011-0.

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Sarabia, Manuel González. "Some bounds for the relative generalized Hamming weights of some evaluation codes." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 2 (2016): 261–70. http://dx.doi.org/10.1515/auom-2016-0041.

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Abstract In this paper we find some bounds for the relative generalized Hamming weights of some codes parameterized by a set of monomials of the same degree. Also we compare the relative generalized Hamming weights of the codes CX(d) and CX′(d) when X′ is embedded in X. We use these results to obtain some lower bounds for the relative generalized Hamming weights of the codes parameterized by the edges of any connected bipartite graph with bipartition (V1, V2) and where |V1| = n1, |V2| = n2, in terms of the relative generalized Hamming weights of the codes associated to the projective tori Tn₁-
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HAWTIN, DANIEL R., NEIL I. GILLESPIE, and CHERYL E. PRAEGER. "ELUSIVE CODES IN HAMMING GRAPHS." Bulletin of the Australian Mathematical Society 88, no. 2 (2013): 286–96. http://dx.doi.org/10.1017/s0004972713000051.

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AbstractWe consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neighbours. We construct a new infinite family of elusive pairs, where the group in question acts transitively on the set of neighbours of the code. In these examples, the alphabet size always divides the length of the code. We show that there is no elusive pair for the smallest set of parameters that does not satisfy this condition. We also pose several questions regarding elusive pairs.
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Phelps, Kevin T., and Mike Levan. "Kernels of nonlinear Hamming codes." Designs, Codes and Cryptography 6, no. 3 (1995): 247–57. http://dx.doi.org/10.1007/bf01388478.

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Dissertations / Theses on the topic "Hamming codes"

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Sabir, Tanveer. "Classification of Perfect codes in Hamming Metric." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-13833.

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The study of coding theory aims to detect and correct the errors during the transmission of the data. It enhances the quality of data transmission and provides better control over the noisy channels.The perfect codes are collected and analyzed in the premises of the Hamming metric.This classification yields that there exists only a few perfect codes. The perfect codes do not guarantee the perfection by all means but just satisfy certain bound and properties. The detection and correction of errors is always very important for better data transmission.
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Muthivhi, Thifhelimbilu Ronald. "Codes Related to and Derived from Hamming Graphs." University of the Western Cape, 2013. http://hdl.handle.net/11394/4091.

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Masters of Science<br>Codes Related to and Derived from Hamming Graphs T.R Muthivhi M.Sc thesis, Department of Mathematics, University of Western Cape For integers n; k 1; and k n; the graph 􀀀k n has vertices the 2n vectors of Fn2 and adjacency de ned by two vectors being adjacent if they di er in k coordinate positions. In particular, 􀀀1 n is the classical n-cube, usually denoted by H1(n; 2): This study examines the codes (both binary and p-ary for p an odd prime) of the row span of adjacency and incidence matrices of these graphs. We rst examine codes of the adjacency matrice
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Harney, Isaiah H. "Colorings of Hamming-Distance Graphs." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/49.

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Hamming-distance graphs arise naturally in the study of error-correcting codes and have been utilized by several authors to provide new proofs for (and in some cases improve) known bounds on the size of block codes. We study various standard graph properties of the Hamming-distance graphs with special emphasis placed on the chromatic number. A notion of robustness is defined for colorings of these graphs based on the tolerance of swapping colors along an edge without destroying the properness of the coloring, and a complete characterization of the maximally robust colorings is given for certai
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Mollard, Michel. "Quelques problèmes combinatoires sur l'hypercube et les graphes de Hamming." Habilitation à diriger des recherches, Grenoble 1, 1989. http://tel.archives-ouvertes.fr/tel-00333335.

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Puchinger, Sven [Verfasser]. "Construction and decoding of evaluation codes in hamming and rank metric / Sven Puchinger." Ulm : Universität Ulm, 2018. http://d-nb.info/1166757323/34.

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Ahmed, Naveed, and Waqas Ahmed. "Classification of perfect codes and minimal distances in the Lee metric." Thesis, Linnaeus University, School of Computer Science, Physics and Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-6574.

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<p>Perfect codes and minimal distance of a code have great importance in the study of theoryof codes. The perfect codes are classified generally and in particular for the Lee metric.However, there are very few perfect codes in the Lee metric. The Lee metric hasnice properties because of its definition over the ring of integers residue modulo q. It isconjectured that there are no perfect codes in this metric for q > 3, where q is a primenumber.The minimal distance comes into play when it comes to detection and correction oferror patterns in a code. A few bounds on the number of codewords and mi
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Faure, Cédric. "Etudes de systèmes cryptographiques construits à l'aide de codes correcteurs, en métrique de Hamming et en métrique rang." Phd thesis, Ecole Polytechnique X, 2009. http://pastel.archives-ouvertes.fr/pastel-00005288.

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Cette thèse étudie deux approches différentes visant à réduire la taille de la clé publique des cryptosystèmes à base de codes correcteurs. Une première idée en ce sens est l'utilisation de familles de codes à haute capacité de correction, comme les codes géométriques. Depuis l'attaque de Sidelnikov et Shestakov, on sait qu'un attaquant peut retrouver la structure d'un code de Reed-Solomon utilisé dans la clé publique. Nous avons réussi à adapter aux courbes hyperelliptiques la méthode d'attaque développée par Minder contre les codes elliptiques. Nous sommes notamment en mesure d'attaquer en t
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Machado, Daniel Alves. "Uma abordagem de dígitos verificadores e códigos corretores no ensino fundamental." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-24112016-103137/.

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Este trabalho, elaborado por meio de pesquisa bibliográfica, apresenta um apanhado sobre os dígitos verificadores presentes no Cadastro de Pessoas Físicas (CPF), no código de barras, e no sistema ISBN; faz uma introdução sobre a métrica de Hamming e os códigos corretores de erros; cita a classe de códigos mais utilizada, que são os códigos lineares, e deixa a sugestão de uma proposta pedagógica para professores de matemática aplicarem no Ensino Fundamental, podendo ser ajustada também para o Ensino Médio. No apêndice A, são propostos alguns exercícios que podem ser trabalhados com os alunos em
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Lemes, Leandro Cruvinel. "Códigos de Goppa e Distâncias Generalizadas de Hamming." Universidade Federal de Uberlândia, 2009. https://repositorio.ufu.br/handle/123456789/16775.

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Fundação de Amparo a Pesquisa do Estado de Minas Gerais<br>In this work, we study geometric Goppa codes and present several results on the so-called generalized Hamming distances. In the particular case of Hermitian codes we present precise results for the first, second and third generalized distances, for almost all Goppa codes supported on one point.<br>Neste trabalho estudamos códigos de Goppa e apresentamos diversos resultados sobre as assim chamadas distâncias generalizadas de Hamming. No caso particular de códigos Hermitianos, apresentamos resultados exatos para a primeira, segunda e ter
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Ávila, Dane Marques de. "O segundo peso de Hamming do código de Reed-Muller generalizado." Universidade Federal de Uberlândia, 2016. https://repositorio.ufu.br/handle/123456789/16822.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>In this work we present the determination of the second Hamming weight of generalized Reed- Muller codes in most cases (see Teorema 4.6). Our main reference is [13], although we have also used results from [3] and [5]. In the first chapter we describe finite fields e we show how they can be constructed. In chapter 2 we present the basics of coding theory. We define what are error correcting codes, the Hamming metric, the parameters of a code, the equivalence of codes through the concept of isometry, and we briefly present generaliz
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Books on the topic "Hamming codes"

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Stergiopoulos, D. G. A recursive soft-decision decoding algorithm for hamming codes. UMIST, 1994.

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Incorporated, Hammond. Hammond ambassador world atlas. Hammond, 1992.

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Hammond ambassador world atlas. Hammond Incorporated, 1989.

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Incorporated, Hammond. Hammond ambassador world atlas. Hammond Incorporated, 1985.

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Hammond Ambassador World Atlas. Hammond World Atlas Corp, 1987.

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Incorporated, Hammond. Hammond Ambassador World Atlas. Hammond World Atlas Corp, 1991.

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Incorporated, Hammond. Hammond Medallion World Atlas: New Final Census Edition Including Zip Codes. Hammond World Atlas Corp, 1986.

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Book chapters on the topic "Hamming codes"

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Schulz, Ralph-Hardo. "Hamming-Codes und erweiterte Hamming-Codes." In Codierungstheorie. Vieweg+Teubner Verlag, 2003. http://dx.doi.org/10.1007/978-3-322-80328-3_12.

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Schulz, Ralph-Hardo. "Hamming-Codes und erweiterte Hamming-Codes." In Codierungstheorie. Vieweg+Teubner Verlag, 1991. http://dx.doi.org/10.1007/978-3-322-91939-7_12.

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Vermani, L. R. "Hamming codes." In Elements of Algebraic Coding Theory. Springer US, 1996. http://dx.doi.org/10.1007/978-1-4899-7268-2_3.

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Houghton, A. D. "Hamming codes." In The Engineer’s Error Coding Handbook. Springer US, 1997. http://dx.doi.org/10.1007/978-1-4613-0447-0_4.

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Vermani, L. R. "Hamming codes." In Elements of Algebraic Coding Theory. Routledge, 2022. http://dx.doi.org/10.1201/9780203758533-3.

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Manz, Olaf. "Hamming- und Golay-Codes." In Fehlerkorrigierende Codes. Springer Fachmedien Wiesbaden, 2016. http://dx.doi.org/10.1007/978-3-658-14652-8_3.

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Childs, Lindsay N. "Matrices and Hamming Codes." In Springer Undergraduate Texts in Mathematics and Technology. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15453-0_7.

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Baylis, John. "The Hamming family and friends." In Error-correcting Codes. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4899-3276-1_6.

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Dejter, Italo, and Kevin Phelps. "Ternary Hamming and binary perfect covering codes." In Codes and Association Schemes. American Mathematical Society, 2001. http://dx.doi.org/10.1090/dimacs/056/08.

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Tromp, John, Louxin Zhang, and Ying Zhao. "Small weight bases for hamming codes." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/bfb0030838.

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Conference papers on the topic "Hamming codes"

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Rurik, William, and Arya Mazumdar. "Hamming codes as error-reducing codes." In 2016 IEEE Information Theory Workshop (ITW). IEEE, 2016. http://dx.doi.org/10.1109/itw.2016.7606865.

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Valles, E. L., A. I. V. Casado, M. Blaum, J. Villasenor, and R. D. Wesel. "Hamming codes are rate-efficient array codes." In GLOBECOM '05. IEEE Global Telecommunications Conference, 2005. IEEE, 2005. http://dx.doi.org/10.1109/glocom.2005.1577866.

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Barta, Janos, and Roberto Montemanni. "Hamming Graphs and Permutation Codes." In 2017 Fourth International Conference on Mathematics and Computers in Sciences and in Industry (MCSI). IEEE, 2017. http://dx.doi.org/10.1109/mcsi.2017.35.

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Ma, Huan, and Lijun Zhang. "LDPC codes based on hamming and BIBD codes." In 2016 IEEE 13th International Conference on Signal Processing (ICSP). IEEE, 2016. http://dx.doi.org/10.1109/icsp.2016.7878139.

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Ordentlich, Erik, and Ron M. Roth. "Hamming-weight constrained coded arrays based on covering codes." In 2013 IEEE International Symposium on Information Theory (ISIT). IEEE, 2013. http://dx.doi.org/10.1109/isit.2013.6620206.

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Weber, J. H., and K. A. S. Abdel-Ghaffar. "Stopping set analysis for Hamming codes." In IEEE Information Theory Workshop, 2005. IEEE, 2005. http://dx.doi.org/10.1109/itw.2005.1531897.

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Ma, Huan, Yangwen Yu, Lijun Zhang, and Lee Lung Cheng. "Hybrid construction of LDPC codes with (14, 8) Hamming code." In 2015 IEEE 9th International Conference on Anti-counterfeiting, Security, and Identification (ASID). IEEE, 2015. http://dx.doi.org/10.1109/icasid.2015.7405682.

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Liu, Shih-Fu, Pedro Reviriego, and Juan Antonio Maestro. "Fault tolerant FIR filters using hamming codes." In 2009 European Conference on Radiation and Its Effects on Components and Systems (RADECS). IEEE, 2009. http://dx.doi.org/10.1109/radecs.2009.5994701.

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Wang, Jyun-Jie, Hong-Da Chen, Ting-Ya Yang, Houshou Chen, and Chi-Yuan Lin. "Data Hiding Technique by Ternary Hamming Codes." In 2013 IEEE 37th Annual Computer Software and Applications Conference (COMPSAC). IEEE, 2013. http://dx.doi.org/10.1109/compsac.2013.28.

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Lim, Jehun, and Young Joon Song. "Optimization of SISO Decoding for Hamming Codes." In CES-CUBE 2015. Science & Engineering Research Support soCiety, 2015. http://dx.doi.org/10.14257/astl.2015.98.02.

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Reports on the topic "Hamming codes"

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Ashikhmin, A. On generalized hamming weighs for Galois ring linear codes. Office of Scientific and Technical Information (OSTI), 1997. http://dx.doi.org/10.2172/515638.

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Mitchell, Gregory. Investigation of Hamming, Reed-Solomon, and Turbo Forward Error Correcting Codes. Defense Technical Information Center, 2009. http://dx.doi.org/10.21236/ada505116.

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