Linear recurring sequences and subfield subcodes of cyclic codes

作     者：GAO ZhiHan FU FangWei 

作者机构：Department of Combinatorics and Optimization University of Waterloo Chern Institute of Mathematics and LPMC Nankai University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2013年第56卷第7期

页      面：1413-1420页

核心收录：

学科分类：11[军事学] 1105[军事学-军队指挥学] 09[农学] 110505[军事学-密码学] 0901[农学-作物学] 

基　　金：supported by National Key Basic Research Program of China(973 Program)(Grant No.2013CB834204) National Natural Science Foundation of China(Grant Nos.61171082 and 10990011) 

主　　题：linear recurring sequences characteristic polynomial cyclic codes subfield subcodes trace codes 

摘      要：Linear recurring sequences over finite fields play an important role in coding theory and cryptography. It is known that subfield subcodes of linear codes yield some good codes. In this paper, we study linear recurring sequences and subfield subcodes. Let Mqm(f(x)) denote the set of all linear recurring sequences over Fqm with characteristic polynomial f(x) over Fqm . Denote the restriction of Mqm(f(x)) to sequences over Fq and the set after applying trace function to each sequence in Mqm(f(x)) by Mqm(f(x)) | Fq and Tr( Mqm(f(x))), respectively. It is shown that these two sets are both complete sets of linear recurring sequences over Fq with some characteristic polynomials over Fq. In this paper, we firstly determine the characteristic polynomials for these two sets. Then, using these results, we determine the generator polynomials of subfield subcodes and trace codes of cyclic codes over Fqm .