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

: HONKALA I

Publisher: ELSEVIER SCIENCE BV

: 1994

: Discrete Applied Mathematics

: DISCRETE APPLIED MATHEMATICS

: DISCRETE APPL MATH

: 52

: 3

: 213

: 221

: 9

: 0166-218X

DOI: https://doi.org/10.1016/0166-218X(94)90141-4

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.

Mathematics