Bounds for Covering Codes over Large Alphabets
Designs, Codes and Cryptography
A note on bounds for q-ary covering codes
IEEE Transactions on Information Theory
Bounds for short covering codes and reactive tabu search
Discrete Applied Mathematics
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Let K"q(n,R) denote the minimal cardinality of a q-ary code of length n and covering radius R. Let @s"q(n,s;r) denote the minimal cardinality of a q-ary code of length n, which is s-surjective with radius r. In order to lower-bound K"q(n,n-2) and @s"q(n,s;s-2) we introduce partition matrices and their transversals. Our approach leads to a short new proof of a classical bound of Rodemich on K"q(n,n-2) and to the new bound K"q(n,n-2)=3q-2n+2, improving the first iff 5==min{2(q+1),K"q(n,R)+1}.