F_q+uF_q+vF_q+uvF_q上的自对偶和LCD双循环码（英文）  

On self-dual and LCD double circulant codes over F_q+uF_q+vF_q+uvF_q

作　　者：卢亚琪 施敏加[1] 伍文婷 肖阿琴 LU Yaqi;SHI Minjia;WU Wenting;XIAO Aqing(School of Mathematical Sciences, Anhui University, Hefei 230601, China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《中国科学技术大学学报》2018年第11期890-897,共8页JUSTC

基　　金：Supported by National Natural Science Foundation of China(61672036);Excellent Youth Foundation of Natural Science Foundation of Anhui Province(1808085J20)

摘　　要：主要研究q为素数的方幂时非链环F_q+uF_q+vF_q+uvF_q,u^2=v^2=0,uv=vu上长度为2n的双循环码.对于给定的正整数n,给出了自对偶和LCD双循环码个数的精确计算公式.利用保距的Gray映射,构造了q为偶数时有限域F_q上长度为8n的自对偶码和LCD码.基于给定的n和q的精确计数公式,由随机编码理论和Artin猜想,得到了关于所研究码的相对距离的修订Varshamov Gilbert界.Double circulant codes of length 2n over a non-chain ring F q+u F q+v F q+uv F q, u 2=v 2=0, uv=vu, were studied when q was a prime power. Exact enumerations of self-dual and LCD double circulant codes for a positive integer n were given. Using a distance-preserving Gray map, self-dual and LCD codes of length 8n over F q were constructed when q was even. Using random coding and the Artin conjecture, the modified Varshamov-Gilbert bounds were derived on the relative distance of the codes considered, building on exact enumeration results for given n and q.

关 键 词：双循环码 自对偶码 LCD码 Artin猜想 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]