On Bases of BCH Codes with Designed Distance 3 and Their Extensions

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Abstract

We consider narrow-sense BCH codes of length pm − 1 over Fp, m ≥ 3. We prove that neither such a code with designed distance δ = 3 nor its extension for p ≥ 5 is generated by the set of its codewords of the minimum nonzero weight. We establish that extended BCH codes with designed distance δ = 3 for p ≥ 3 are generated by the set of codewords of weight 5, where basis vectors can be chosen from affine orbits of some codewords.

Original languageEnglish
Pages (from-to)309-316
Number of pages8
JournalProblems of Information Transmission
Volume56
Issue number4
DOIs
Publication statusPublished - Dec 2020

Keywords

  • affine-invariant code
  • BCH code
  • cyclic code
  • minimum weight basis
  • single orbit affine generator

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