The Nonexistence of Ternary \((231, 6, 153)\) Codes

It is known (cf. {Hamada} [12] and {BrouwerEupen} and van Eupen [2] ) that (1) there is no ternary \([230, 6, 153]\) code meeting the Griesmer bound but (2) there exists a ternary \([232, 6, 153]\) code. This implies that \(n_3(6, 153) = 231\) or \(232\), where \(n_3(k, d)\) denotes the smallest value of \(n\) for which there exists a ternary \([n, k, d]\) code. The purpose of this paper is to prove that \(n_3(6, 153) = 232\) by proving the nonexistence of ternary \([231, 6, 153]\) codes.