On ( q, 1)-subnormal q-ary covering codes

Abstract

We show that if q ≠ 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.