Ternary primitive LCD BCH codes
Information Theory
2021-04-12 v1 math.IT
Abstract
Absolute coset leaders were first proposed by the authors which have advantages in constructing binary LCD BCH codes. As a continue work, in this paper we focus on ternary linear codes. Firstly, we find the largest, second largest, and third largest absolute coset leaders of ternary primitive BCH codes. Secondly, we present three classes of ternary primitive BCH codes and determine their weight distributions. Finally, we obtain some LCD BCH codes and calculate some weight distributions. However, the calculation of weight distributions of two of these codes is equivalent to that of Kloosterman sums.
Cite
@article{arxiv.2104.04193,
title = {Ternary primitive LCD BCH codes},
author = {Xinmei Huang and Qin Yue and Yansheng Wu and Xiaoping Shi},
journal= {arXiv preprint arXiv:2104.04193},
year = {2021}
}
Comments
16 pages. To appear in Advances in Mathematics of Communications