Extendability of 3-weight (mod q) linear codes over Fq

AbstractAn [n,k,d]q code is called w-weight (mod q) if there are w integers i1,i2,…,iw∈{0,1,2,…,q−1} such that any weight i of the codewords satisfies i≡ij(modq) for some j. We consider 3-weight (mod q) [n,k,d]q codes with d≡−1(modq) whose weights are congruent to 0 or ±1(modq). We show that such codes are extendable when q is even and that there are some types of such codes which are always extendable when q is odd. The latter is a generalization of the result on the extendability of ternary linear codes [T. Maruta, Extendability of ternary linear codes, Des. Codes Cryptogr. 35 (2005) 175–190] to q-ary linear codes with q odd