A1 Journal article – refereed

ON (Q,1)-SUBNORMAL Q-ARY COVERING CODES

List of Authors: HONKALA I

Publisher: ELSEVIER SCIENCE BV

Publication year: 1994

Journal: Discrete Applied Mathematics

Journal name in source: DISCRETE APPLIED MATHEMATICS

Journal acronym: DISCRETE APPL MATH

Volume number: 52

Issue number: 3

ISSN: 0166-218X

Abstract

We show that if q not-equal 3 is a prime power and there exists a (q, n, M) 1 code, i.e., a q-ary code of length n with M codewords and covering radius 1 then there exists also a (q, 1)-subnormal (q, qn + 1, q((q-1)n)M) 1 code. We also show that all nontrivial linear q-ary codes with covering radius 1 are (q, 1)-subnormal with the exception of the ternary [4, 2]1 Hamming code.