The paper shows that if 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 code. It also shows 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.
