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 \(K_4(5,2) \geq 14\) and \(K_4(6,2) \geq 32\).