标题：On self-duality and hulls of cyclic codes over F(2)m[u]/< u(k)> with oddly even length
作者：Cao, Yonglin; Cao, Yuan; Fu, Fang-Wei
作者机构：[Cao, Yonglin; Cao, Yuan] Shandong Univ Technol, Sch Math & Stat, Zibo 255091, Shandong, Peoples R China.; [Cao, Yuan] Hubei Univ, Fac Math & Stat, 更多
通讯作者：Cao, Y;Cao, Y;Cao, Y
通讯作者地址：[Cao, Y]Shandong Univ Technol, Sch Math & Stat, Zibo 255091, Shandong, Peoples R China;[Cao, Y]Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, W 更多
来源：APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
关键词：Cyclic code; Self-dual code; Hull; Self-orthogonal code; Finite chain; ring
摘要：Let F2m be a finite field of 2melements and denote R=F2m[u]=F2m+uF2m++uk-1F2m, where k is an integer satisfying k >= 2. For any odd positive integer n, an explicit representation for every self-dual cyclic code over R of length 2n and a mass formula to count the number of these codes are given. In particular, a generator matrix is provided for the self-dual 2-quasi-cyclic code of length 4n over F2m derived by an arbitrary self-dual cyclic code of length 2n over F2m+uF2m and a Gray map from F2m+uF2m Finally, the hull of each cyclic code with length 2n over F2m+uF2m is determined and all distinct self-orthogonal cyclic codes of length 2n over F2m+uF2(m) are listed.