Generalized Hamming weights of trace codes

Author

Stichtenoth, Henning ; Voss, Clare

Author_Institution

Dept. of Math. & Inf., Essen Univ., Germany

Volume

40

Issue

2

fYear

1994

fDate

3/1/1994 12:00:00 AM

Firstpage

554

Lastpage

558

Abstract

Linear codes over F_p often admit a natural representation as trace codes of codes that are defined over an extension field F_pm. In the paper, the authors obtain estimates for the weights of subcodes of such trace codes. Their main result is a far-reaching generalization of the Carlitz-Uchiyama bound for the duals of binary BCH codes. In particular, they prove sharp bounds for the generalized Hamming weights of a large class of codes, including duals of BCH codes, classical Goppa codes, Melas codes, and arbitrary cyclic codes of length n=p^m-1. The main tool is the theory of algebraic functions over finite fields, in particular the Hasse-Weil bound for the number of places of degree one

Keywords

BCH codes; algebra; cyclic codes; error correction codes; Carlitz-Uchiyama bound; Hasse-Weil bound; Melas codes; algebraic functions; binary BCH codes; classical Goppa codes; cyclic codes; extension field; generalized Hamming weight; linear codes; subcodes; trace codes; Decoding; Error correction; Error correction codes; Galois fields; Hamming weight; Lattices; Linear code; Reed-Solomon codes;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.312185

Filename

312185