TY - JOUR

T1 - On Bases of BCH Codes with Designed Distance 3 and Their Extensions

AU - Mogilnykh, I. Yu

AU - Solov’eva, F. I.

N1 - 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: © 2020, Pleiades Publishing, Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2020/12

Y1 - 2020/12

N2 - 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.

AB - 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.

KW - affine-invariant code

KW - BCH code

KW - cyclic code

KW - minimum weight basis

KW - single orbit affine generator

UR - http://www.scopus.com/inward/record.url?scp=85099996084&partnerID=8YFLogxK

U2 - 10.1134/S003294602004002X

DO - 10.1134/S003294602004002X

M3 - Article

AN - SCOPUS:85099996084

VL - 56

SP - 309

EP - 316

JO - Problems of Information Transmission

JF - Problems of Information Transmission

SN - 0032-9460

IS - 4

ER -