A Note on Characteristic Generators of a Free Cyclic Code and Its Dual

作     者：YANG Qinqin QIN Zhongping 

作者机构：School of Computer Wuhan University Wuhan 430072 Huibei China School of Software Huazhong University of Science and Technology Wuhan 430074 Hubei China 

出 版 物：《Wuhan University Journal of Natural Sciences》 (武汉大学学报（自然科学英文版）)

年 卷 期：2009年第14卷第1期

页      面：14-18页

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 080801[工学-电机与电器] 0808[工学-电气工程] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(60673071) 

主　　题：Hensel lift cyclic codes characteristic generators trellises state-complexity profile 

摘      要：Let C be a free cyclic code over Zp^a and dim pC = k. In the paper, we prove that if the k characteristic generators of C are p-linearly independent then the corresponding nα- k characteristic generators of C^⊥ are p-linearly independent. We then show that to any trellis that can be constructed from k p-linearly independent characteristic generators of C, there exists a trellis for C^⊥ with the same state-complexity profile, which generalizes the conjecture of Koetter and Vardy to a free cyclic code over Zpo.