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 language | English |
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Pages (from-to) | 309-316 |
Number of pages | 8 |
Journal | Problems of Information Transmission |
Volume | 56 |
Issue number | 4 |
DOIs | |
Publication status | Published - Dec 2020 |
Keywords
- affine-invariant code
- BCH code
- cyclic code
- minimum weight basis
- single orbit affine generator