Single orbit affine generators for extended BCH codes with designed distance three

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Abstract

We show that for any prime p, p ≠ 2, 3 and any m, m ≥ 3 the narrow-sense BCH codes over GF (p) of length pm - 1 with designed distance three are not spanned by theirs minimum nonzero weight codewords. We prove that the extensions of these codes are spanned by their codewords of weight five and the bases could be chosen in the affine orbits of explicit codewords.

Original languageEnglish
Title of host publicationProceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages110-112
Number of pages3
ISBN (Electronic)9781665402873
DOIs
Publication statusPublished - 11 Oct 2020
Event17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020 - Vitual, Albena, Bulgaria
Duration: 11 Oct 202017 Oct 2020

Publication series

NameProceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020

Conference

Conference17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020
CountryBulgaria
CityVitual, Albena
Period11.10.202017.10.2020

Keywords

  • affine group
  • BCH code
  • minimum weight codewords
  • single orbit generator

OECD FOS+WOS

  • 1.02 COMPUTER AND INFORMATION SCIENCES
  • 1.01 MATHEMATICS

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