Some improvements to the extendability of ternary linear codes

For a ternary [n,k,d][n,k,d] code CC with d≡1d≡1 or 2 (mod 3), k⩾3k⩾3, the diversity (Φ0,Φ1)(Φ0,Φ1) given byΦ0=12∑3|i,i≠0Ai,Φ1=12∑i≢0,d(mod3)Ai is important to know about the extendability of CC, where AiAi stands for the number of codewords with weight i  . As a continuation of [T. Maruta, Extendability of ternary linear codes, Des. Codes Cryptogr. 35 (2005) 175–190], we prove all the conjectures posed in this paper, which yield some improvements to the extendability and non-extendability of ternary linear codes. We also give the necessary and sufficient conditions for the extendability of CC for the case when k=4k=4.