LCD MDS码的几类构造方法  

Several constructions of LCD MDS codes

作　　者：金玲飞 孙中华[2] 滕佳明 Lingfei Jin;Zhonghua Sun;Jiaming Teng

机构地区：[1]复旦大学计算机科学技术学院,上海201203 [2]合肥工业大学数学学院,合肥230601

出　　处：《中国科学：数学》2021年第10期1463-1484,共22页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11501117和62002093);上海市科委启明星计划(批准号:20QA1401100)资助项目。

摘　　要：线性互补对偶(linear complementary dual, LCD)码因其在数据存储和密码学方面的显著作用而受到广泛研究.线性互补对偶极大距离可分(LCD MDS (maximum distance separable))码具有最大的纠错能力,因而,构造LCD MDS码是LCD码理论研究的一个热点. Carlet等利用线性码的生成矩阵给出了LCD MDS码的存在性结果.最近,编码学者们基于广义Reed-Solomon码、代数几何码和常循环码等给出了LCD MDS码的显式构造.本文将介绍构造LCD MDS码的主要方法、结果以及最新进展.Linear complementary dual codes(LCD codes) have been widely studied because of their significant role in data storage and cryptography. Maximum distance separable codes with complimentary duals(LCD MDS codes) have the greatest error correcting ability, and so the construction of LCD MDS codes is a hot topic. By using the generator matrix of linear codes, the existence results of LCD MDS codes are given by Carlet et al. in 2018. Recently, several display constructions of LCD MDS codes are given by scholars via the generalized ReedSolomon codes, the algebraic geometry codes, the constacylic codes and so on. In this paper, we will introduce the main methods, results and recent progress of constructing LCD MDS codes.

关 键 词：线性互补对偶码 MDS码 REED-SOLOMON码 

分 类 号：O157.4[理学—数学]