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

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 p m − 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...

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Vydáno v:2020 Algebraic and Combinatorial Coding Theory (ACCT) s. 1 - 3
Hlavní autoři: Mogilnykh, Ivan, Solov'eva, Faina
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 11.10.2020
Témata:
affine group
BCH code
Generators
Information theory
minimum weight codewords
Orbits
single orbit generator
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Shrnutí: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 p m − 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.
DOI:10.1109/ACCT51235.2020.9383376