与三元广义 Reed-Muller 码子码相关联的 2-设计的线性码
信息论
2019-07-31 v1 math.IT
摘要
本文计算了 [C. Ding, C. Li, Infinite families of 2-designs and 3-designs from linear codes, Discrete Mathematics 340(10) (2017) 2415--2431] 中所考虑的一类三元线性码中由最小权码字支撑的 2-设计的关联矩阵的三秩。推导了由这些设计的关联矩阵张成的三元码的最小距离下界,并证明这些码是 4 阶广义 Reed-Muller 码的子码。
引用
@article{arxiv.1907.13032,
title = {Linear codes of 2-designs associated with subcodes of the ternary generalized Reed-Muller codes},
author = {Cunsheng Ding and Chunming Tang and Vladimir D. Tonchev},
journal= {arXiv preprint arXiv:1907.13032},
year = {2019}
}