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