西北师范大学学报（自然科学版）2026，Vol.62Issue(1)：41-48,8.DOI:10.16783/j.cnki.nwnuz.2026.01.005
几类MDS码和NMDS码的构造
Construction of several classes of MDS codes and NMDS codes
摘要
Abstract
MDS codes are optimal linear codes whose parameters achieve the Singleton bound.They are widely applied to distributed storage systems,random error channels and other related fields.NMDS codes have emerged as one of the hotspots in coding theory,as they can significantly reduce complexity of encoding and decoding while maintaining nearly the same error correction performance.The matrix is constructed by selecting the elements of the unit circle over finite field Fq2(where q is a power of 2).And a column vector is added to obtain a new matrix,which is used as a generator matrix to construct MDS codes and NMDS codes with length of(q+2).The weight enumerators of the constructed NMDS codes are determined.Then,subsets of Fqt(where t≥1 is an integer)of size l(4<l≤qt)are selected to construct MDS codes with length of l.The research shows that all MDS codes constructed are Griesmer codes,and all NMDS codes are near Griesmer codes.Meanwhile,the codebook indicates that all codes obtained are new.关键词
MDS码/NMDS码/重量计数器/Griesmer界Key words
MDS code/NMDS code/weight enumerator/Griesmer bound分类
数理科学引用本文复制引用
杜小妮,薛婧,乔兴斌,赵紫薇..几类MDS码和NMDS码的构造[J].西北师范大学学报（自然科学版）,2026,62(1):41-48,8.基金项目
国家自然科学基金资助项目(62562055,62172337) （62562055,62172337）
甘肃省自然科学基金重点资助项目(23JRRA685) （23JRRA685）
甘肃省基础研究创新群体资助项目(23JRRA684) （23JRRA684）
