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

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 cove ring 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.