Title :
Generalized Hamming Weights of Irreducible Cyclic Codes
Author :
Minghui Yang ; Jin Li ; Keqin Feng ; Dongdai Lin
Author_Institution :
State Key Lab. of Inf. Security, Inst. of Inf. Eng., Beijing, China
Abstract :
The generalized Hamming weights dr(C) of a linear code C are a natural generalization of the minimum Hamming distance d(C)[=d1(C)] and have become an important research object in coding theory since Wei´s originary work in 1991. In this paper, two general formulas on d(C) for irreducible cyclic codes are presented using Gauss sums and the weight hierarchy {d1(C), d2(C), ... , dk(C)} (k= dim C) is completely determined for several cases.
Keywords :
Hamming codes; cyclic codes; linear codes; number theory; Gauss sums; coding theory; generalized Hamming weights; irreducible cyclic codes; linear code; natural minimum Hamming distance generalization; weight hierarchy; Additives; Hamming distance; Hamming weight; Linear codes; Next generation networking; Polynomials; Gauss sum; Generalized Hamming weight; generalized Hamming weight; irreducible cyclic code;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2015.2444013
