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 recurrin...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 .展开更多
The relative subcodes are closely related to the concept of the relative generalized Hamming weight. Using projective geometry methods and the concept of the relative generalized Hamming weight, the authors prove a pr...The relative subcodes are closely related to the concept of the relative generalized Hamming weight. Using projective geometry methods and the concept of the relative generalized Hamming weight, the authors prove a property of the relative subcodes which substantially improves the existing result.展开更多
In this paper, the subspace subcodes of generalized Reed-Solomn codes are codes are introduced and the fomulas to compute the dimensions of these codes are given.
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)
文摘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 .
基金This research is supported by the National Natural Science Foundation of China under Grant Nos. 60972033 and 60832001.
文摘The relative subcodes are closely related to the concept of the relative generalized Hamming weight. Using projective geometry methods and the concept of the relative generalized Hamming weight, the authors prove a property of the relative subcodes which substantially improves the existing result.
文摘In this paper, the subspace subcodes of generalized Reed-Solomn codes are codes are introduced and the fomulas to compute the dimensions of these codes are given.
