The nonexistence of ternary [97,6,63] codes

Abstract It has been shown by Gulliver (Discrete Math. 149 (1996) 83) that there exists a ternary [98,6,63] code. But it is unknown whether or not there exists a ternary [97,6,63] code. The purpose of this paper is to prove that there is no ternary [97,6,63] code using the structure of a {267,87;5,3}-minihyper and a generator matrix of a ternary [97,6,63] code. Since n 3 (6,63)=97 or 98 and d 3 (97,6)=62 or 63, this implies that n 3 (6,63)=98 and d 3 (97,6)=62, where n 3 ( k , d ) and d 3 ( 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(3).