A1 Refereed original research article in a scientific journal
ON (Q,1)-SUBNORMAL Q-ARY COVERING CODES
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: 52
Issue: 3
First page : 213
Last page: 221
Number of pages: 9
ISSN: 0166-218X
DOI: https://doi.org/10.1016/0166-218X(94)90141-4(external)
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.
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.