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This article is cited in 2 scientific papers (total in 2 papers)
Coding Theory
On bases of BCH codes with designed distance $3$ and their extensions
I. Yu. Mogilnykhabc, F. I. Solov'evaab a Sobolev Institute of Mathematics, Siberian Branch
of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Regional Scientific and Educational Mathematical Center,
Tomsk State University, Tomsk, Russia
Abstract:
We consider narrow-sense BCH codes of length $p^m-1$ over ${{\mathbb{F}}}_{p}$, $m\geqslant3$. We prove that neither such a code with designed distance $\delta=3$ nor its extension for $p\geqslant5$ is generated by the set of its codewords of the minimum nonzero weight. We establish that extended BCH codes with designed distance $\delta=3$ for $p\geqslant3$ are generated by the set of codewords of weight $5$, where basis vectors can be chosen from affine orbits of some codewords.
Keywords:
BCH code, cyclic code, affine-invariant code, minimum weight basis, single orbit affine generator.
Received: 10.07.2020 Revised: 26.10.2020 Accepted: 27.10.2020
Citation:
I. Yu. Mogilnykh, F. I. Solov'eva, “On bases of BCH codes with designed distance $3$ and their extensions”, Probl. Peredachi Inf., 56:4 (2020), 10–18; Problems Inform. Transmission, 56:4 (2020), 309–316
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https://www.mathnet.ru/eng/ppi2325 https://www.mathnet.ru/eng/ppi/v56/i4/p10
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Abstract page: | 101 | Full-text PDF : | 6 | References: | 19 | First page: | 8 |
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