Lower Bounds For Quaternary Covering Codes

Abstract

Let $K_q(n,R)$ denote the least cardinality of a $q$-ary code of length $n$, such that every $q$-ary word of length $n$ differs from at least one word in the code in at most $R$ places. We use a method of Blass and Litsyn to derive the bounds $K_4(5,2)\ge 14$ and $K_4(6,2)\ge 32$.