Abstract
We consider narrow-sense BCH codes of length pm − 1 over \({{\mathbb{F}}}_{p}\), 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.
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The authors are grateful to a reviewer for a number of comments and suggestions, which helped them to improve the presentation.
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The research was supported in part by the Ministry of Science and Higher Education of the Russian Federation, contract no. 075-02-2020-1479/1.
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Mogilnykh, I., Solov’eva, F. On Bases of BCH Codes with Designed Distance 3 and Their Extensions. Probl Inf Transm 56, 309–316 (2020). https://doi.org/10.1134/S003294602004002X
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DOI: https://doi.org/10.1134/S003294602004002X