一类新的MDS symbol-pair码  

A New Class of MDS symbol-pair Codes

作　　者：王雪梅 张家骏[2] WANG Xuemei;ZHANG Jiajun(School of Mathematics and Statistics,Zaozhuang University,Zaozhuang 277160,China;School of Artificial Intelligence,Zaozhuang University,Zaozhuang 277160,China)

机构地区：[1]枣庄学院数学与统计学院,山东枣庄277160 [2]枣庄学院人工智能学院,山东枣庄277160

出　　处：《枣庄学院学报》2023年第2期10-15,共6页Journal of Zaozhuang University

基　　金：山东省自然科学基金资助项目(ZR2021MA046)。

摘　　要：为了对抗符号对(symbol-pair)读取信道中的符号对错误,符号对码应运而生。与经典纠错码类似,极小对距离越大,符号对码的纠错能力越强,因此,构造具有较大极小符号对距离的符号对码至关重要。根据多项式重根的判别方法,通过分析有限域F p上线性方程组的解,得到了一类最大距离可分的符号对(MDS symbol-pair)码,其长度为4 p,极小符号对距离为10。结果表明,在同样码长的情况下,新构造的MDS符号对码具有较大的极小符号对距离。symbol-pair codes are designed to protect against pair-errors in data reading channels.Similar to classical error correction code,maximum distance separable(MDS)symbol-pair codes have the best error-correcting capability,so the construction of MDS symbol-pair codes is crucial in symbol-pair coding theory.In this paper,according to a method for distinguishing multiple roots of polynomials,we derive a new class of MDS symbol-pair codes with length of 4pand minimum symbol-pair distance of ten by analyzing the solutions of certain equations over finite fields.The result shows that our new MDS symbol-pair codes have a large minimum symbol-pair distance in the MDS symbol-pair codes with equal length.

关 键 词：MDS符号对码 极小符号对距离 常循环码 重根循环码 

分 类 号：O153.4[理学—数学]