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.

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