A new extension theorem for ternary linear codes and its application

摘要

An [n, k, d](q) code is a linear code of length n, dimension k and minimum weight d over the field of q elements. An [n, k, d], code C is called extendable if C can be extended to an [n + 1, k, d + 1](q) code. We give a new extension theorem for ternary linear codes. As an application, we prove the non-existence of [512, 6, 340](3) code, which is a new result. (C) 2020 Elsevier Inc. All rights reserved.