基于2个不相交子集的MDS自对偶码构造  

New MDS self-dual codes based on two disjoint subsets

作　　者：曹宇婷 朱士信[1] CAO Yuting;ZHU Shixin(School of Mathematics,Hefei University of Technology,Hefei 230601,China)

机构地区：[1]合肥工业大学数学学院,安徽合肥230601

出　　处：《合肥工业大学学报（自然科学版）》2024年第1期132-136,共5页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(12171134);国家自然科学基金联合基金资助项目(U21A20428)。

摘　　要：最大距离可分(maximum distance separable, MDS)自对偶码是一类最优线性码,在通信、数据存储和区组设计等领域有着广泛的应用,构造MDS自对偶码是当前编码理论研究的一个热点问题。文章基于有限域及其乘法群的2个不相交子集,利用广义Reed-Solomon(RS)码构造了几类新的MDS自对偶码;得到的MDS自对偶码具有灵活的长度。Maximum distance separable(MDS)self-dual codes are a class of optimal linear codes,which can be extensively applied in many fields such as communications,data storage and block designs.It has become a hot topic to construct MDS self-dual codes in coding theory.In this paper,several new classes of MDS self-dual codes are constructed from generalized Reed-Solomon(RS)codes based on two disjoint subsets of the multiplicative subgroup of a finite field.The resulting MDS self-dual codes have flexible lengths.

关 键 词：最大距离可分(MDS)自对偶码 广义Reed-Solomon(RS)码 有限域 

分 类 号：O157.4[理学—数学]