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New Families Of Triple Error Correcting Codes With Bch Parameters

Help pages Full-text links: Download: PDF PostScript Other formats (license) Current browse context: cs.IT new| recent| 0803Change to browse by: cs cs.DM math References & CitationsNASA ADS DBLP - CS Bibliography listing | bibtex Carl Bracken Bookmark (what is this?) Computer Science > Information Theory Title: New Families of Triple Error Correcting Codes with BCH Parameters Authors: Carl Bracken (Submitted on 25 Mar 2008) Abstract: Discovered by Bose, Chaudhuri and Hocquenghem, the BCH family of error correcting codes are one of the most studied families in coding theory. They are also among the best performing codes, particularly when the number of errors being corrected is small relative to the code length. In this article we consider binary codes with minimum distance of 7. We construct new families of codes with these BCH parameters via a generalisation of the Kasami-Welch Theorem. Comments: 11 pages. Submitted to IEEE Transactions on information Theory Subjects: Information Theory (cs.IT); Discrete Mathematics (cs.DM) Citeas: arXiv:0803.3553 [cs.IT] (or arXiv:0803.3553v1 [cs.IT] for this version) Submission history From: Carl Bracken [view email] [v1] Tue, 25 Mar 2008 13:08:19 GMT (6kb) Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?) Link back to: arXiv, form interface, contact.

triple-error-correcting BCH-like code and some minimum distance resultsAuthorsAuthors and affiliationsCarl BrackenFaruk GöloğluEmail authorArticleFirst Online: 13 November 2012Received: 23 March 2012Revised: 13 October 2012Accepted: 20 October 2012DOI: 10.1007/s10623-012-9763-6Cite this article as: Bracken, C. & Göloğlu, F. Des. Codes Cryptogr. (2014) 72: 317. doi:10.1007/s10623-012-9763-6 264 Views AbstractIn this paper, we give the first example of a non-cyclic triple-error-correcting code which is not equivalent to the primitive http://arxiv.org/abs/0803.3553 BCH code. It has parameters [63, 45, 7]. We also give better bounds on minimum distances of some [2n − 1, 2n - 3n - 1] cyclic codes with three small zeroes. Finally, we reprove weight distribution results of Kasami for triple-error-correcting BCH-like codes using direct methods.KeywordsBCH codesMinimum http://link.springer.com/article/10.1007/s10623-012-9763-6 distanceCyclic codesAPN functionsCommunicated by J. D. Key.Mathematics Subject Classification (2000)68P3094B1506E30References1.Berlekamp E.R.: The weight enumerators for certain subcodes of the second order binary Reed-Muller codes. Inf. Control. 17, 485–500 (1970)CrossRefMATHMathSciNetGoogle Scholar2.Bose R.C., Ray-Chaudhuri D.K.: On a class of error correcting binary group codes. Inf. Control. 3, 68–79 (1960)CrossRefMATHMathSciNetGoogle Scholar3.Bracken C., Byrne E., Markin N., McGuire G.: Determining the nonlinearity of a new family of APN functions. In: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, vol. 4851 of Lecture Notes in Computer Science, pp. 72–79. Springer, Berlin, (2007).4.Browning K.A., Dillon J.F., Kibler R.E., McQuistan M.T.: APN polynomials and related codes. J. Comb. Inf. Syst. Sci. 34(1–4), 135–159 (2009)MATHGoogle Scholar5.Bosma W., Cannon J., Playoust C.: The Magma algebra system. I. The user language. J. Symb. Comput. 24, 235–265 (1997)CrossRefMATHMathSciNetGoogle Scholar6.Carlet C., Charpin P., Zinoviev V.: Codes, bent functions and permutations suitable for DES-like cryptosystems. De

the article in the profile.DoneDuplicate citationsThe following articles are merged in Scholar. Their combined citations http://scholar.google.com/citations?user=dvJJ2L8AAAAJ&hl=en are counted only for the first article.DoneMerge duplicatesCitations http://dblp.uni-trier.de/pers/b/Bracken:Carl per yearScholarFollowEmailFollow new articlesFollow new citationsCreate alertCancelCarl BrackenSenior research fellow, Nanyang technological UniverstitCombinatorics, finite fields, coding theory, cryptographyVerified email at ntu.edu.sgScholarGet my own profileGoogle ScholarCitation indicesAllSince 2011Citations393311h-index109i10-index107200820092010201120122013201420152016162330753157712948Title1–20Cited byYearNew families of quadratic almost perfect nonlinear new families trinomials and multinomialsC Bracken, E Byrne, N Markin, G McguireFinite Fields and Their Applications 14 (3), 703-714, 2008852008A highly nonlinear differentially 4 uniform power mapping that permutes fields of even degreeC Bracken, G LeanderFinite Fields and Their Applications 16 (4), 231-242, 2010562010A new families of few more quadratic APN functionsC Bracken, E Byrne, N Markin, G McGuireCryptography and Communications 3 (1), 43-53, 2011462011Binomial differentially 4 uniform permutations with high nonlinearityC Bracken, CH Tan, Y TanFinite Fields and Their Applications 18 (3), 537-546, 2012352012Determining the nonlinearity of a new family of APN functionsC Bracken, E Byrne, N Markin, G McGuireInternational Symposium on Applied Algebra, Algebraic Algorithms, and Error ..., 2007322007Triple-error-correcting BCH-like codesC Bracken, T Helleseth2009 IEEE International Symposium on Information Theory, 1723-1725, 2009152009New quasi-symmetric designs constructed using mutually orthogonal Latin squares and Hadamard matricesC Bracken, G McGuire, H WardDesigns, Codes and Cryptography 41 (2), 195-198, 2006132006On the Walsh spectrum of a new APN functionC Bracken, E Byrne, N Markin, G McGuireIMA International Conference on Cryptography and Coding, 92-98, 2007122007On the equivalence

Carl Bracken export bibliographyBibTeXRISRDF N-TriplesRDF/XMLXMLRSSdblp keysdblp key:homepages/83/6717ask othersGoogleGoogle ScholarMS Academic SearchCiteSeerXSemantic Scholarshare bibliographyTwitterRedditBibSonomyLinkedInGoogle+Facebookshort URL:http://dblp.org/pid/83/6717help usHow can I correct errors in dblp?contact dblp '10'00 Trier 1Trier 2Dagstuhl by yearby typeclassic > Home > Persons Refine list refinements active!zoomed in on ?? of ?? records dismiss all constraintsshowing all ?? records 2010 - today see FAQWhat is the meaning of the colors in the publication lists?2014[j14]viewelectronic edition via DOIexport recordBibTeXRISRDF N-TriplesRDF/XMLXMLdblp key:journals/dcc/BrackenG14ask othersGoogleGoogle ScholarMS Academic SearchCiteSeerXSemantic Scholarshare recordTwitterRedditMendeleyBibSonomyLinkedInGoogle+Facebookshort URL:http://dblp.org/rec/journals/dcc/BrackenG14Carl Bracken, Faruk Göloglu: A non-cyclic triple-error-correcting BCH-like code and some minimum distance results. Des. Codes Cryptography 72(2): 317-330 (2014)[j13]viewelectronic edition via DOIexport recordBibTeXRISRDF N-TriplesRDF/XMLXMLdblp key:journals/ffa/BrackenTT14ask othersGoogleGoogle ScholarMS Academic SearchCiteSeerXSemantic Scholarshare recordTwitterRedditMendeleyBibSonomyLinkedInGoogle+Facebookshort URL:http://dblp.org/rec/journals/ffa/BrackenTT14Carl Bracken, Chik How Tan, Yin Tan: On a class of quadratic polynomials with no zeros and its application to APN functions. Finite Fields and Their Applications 25: 26-36 (2014)2012[j12]viewelectronic edition via DOIexport recordBibTeXRISRDF N-TriplesRDF/XMLXMLdblp key:journals/ffa/BrackenTT12ask othersGoogleGoogle ScholarMS Academic SearchCiteSeerXSemantic Scholarshare recordTwitterRedditMendeleyBibSonomyLinkedInGoogle+Facebookshort URL:http://dblp.org/rec/journals/ffa/BrackenTT12Carl Bracken, Chik How Tan, Yin Tan: Binomial differentially 4 uniform permutations with high nonlinearity. Finite Fields and Their Applications 18(3): 537-546 (2012)[c4]viewelectronic edition via DOIexport recordBibTeXRISRDF N-TriplesRDF/XMLXMLdblp key:conf/isit/BrackenCP12ask othersGoogleGoogle ScholarMS Academic SearchCiteSeerXSemantic Scholarshare recordTwitterRedditMendeleyBibSonomyLinkedInGoogle+Facebookshort URL:http://dblp.org/rec/conf/isit/BrackenCP12Carl Bracken, Yeow Meng Chee, Punarbasu Purkayastha: Optimal family of q-ary codes obtained from a substructure of generalised Hadamard

 

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