Some improvements to the extendability of ternary linear codes

For a ternary [n, k, d] code C with d ≡ 1 or 2 (mod 3), k 3, the diversity (Φ0,Φ1) given by Φ0 = 1 2 ∑ 3|i, i =0 Ai, Φ1 = 1 2 ∑ i ≡0, d (mod 3) Ai is important to know about the extendability of C, where Ai 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 C for the case when k = 4. © 2005 Elsevier Inc. All rights reserved.