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
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