@article{954fa96b1b904c7fa3dd70f0585d5d39,
title = "On Bases of BCH Codes with Designed Distance 3 and Their Extensions",
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.",
keywords = "affine-invariant code, BCH code, cyclic code, minimum weight basis, single orbit affine generator",
author = "Mogilnykh, {I. Yu} and Solov{\textquoteright}eva, {F. I.}",
note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2020",
month = dec,
doi = "10.1134/S003294602004002X",
language = "English",
volume = "56",
pages = "309--316",
journal = "Problems of Information Transmission",
issn = "0032-9460",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "4",
}