The Nonexistence of Quaternary Linear Codes With Parameters \([243,5,181], [248,5,185]\) and \([240,5,179]\)

Let \(n_4(k,d)\) and \(d_4(n, k)\) denote the smallest value of \(n\) and the largest value of \(d\), respectively, for which there exists an \([n, k, d]\) code over the Galois field \(GF(4)\). It is known (cf. Boukliev [1] and Table B.2 in Hamada [6]) that (1) \(n_4(5, 179) =240\) or \(249\), \(n_4(5,181) = 243\) or \(244, n_4(5, 182) = 244\) or \(245, n_4(5, 185) = 248\) or \(249\) and (2) \(d_4(240,5) = 178\) or \(179\) and \(d_4(244,5) = 181\) or \(182\). The purpose of this paper is to prove that (1) \(74(5,179) = 241, n_4(5,181) = 244, n_4(5,182) = 245, n_4(5, 185) = 249\) and (2) \(d_4(240, 5) = 178\) and \(d_4(244,5) = 181\).