Single orbit affine generators for extended BCH codes with designed distance three - Mogilnykh, Ivan; Solov'eva, Faina (2020 Algebraic and Combinatorial Coding Theory (ACCT), 2020)
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.