New results on codes with covering radius 1 and minimum distance 2
The minimal cardinality of a q-ary code of length n and covering radius at most R is denoted by K-q(n, R); if we have the additional requirement that the minimum distance be at least d, it is denoted by K-q(n, R, d). Obviously, K-q(n, R, d) >= K-q(n, R). In this paper, we study instances for which K-q(n,1,2) > K-q(n, 1) and, in particular, determine K-4(4,1,2)=28 > 24=K-4(4,1).
covering radius minimum distance coding theory quaternary codes complete classification