On the generalized Hamming weights of several classes of cyclic cods

Author

Feng, G.L. ; Tzeng, K.K. ; Wei, V.K.

Author_Institution

Dept. of Comput. Sci. & Electr. Eng., Lehigh Univ., Bethlehem, PA, USA

Volume

38

Issue

3

fYear

1992

fDate

5/1/1992 12:00:00 AM

Firstpage

1125

Lastpage

1130

Abstract

The generalized Hamming weights of a linear code are fundamental code parameters related to the minimal overlap structures of the subcodes. They were introduced by V.K. Wei (1991) and shown to characterize the performance of the linear code in certain cryptographical applications. Results are presented on the generalized Hamming weights of several classes of binary cyclic codes, including primitive double-error-correcting and triple-error-correcting BCH codes, certain reversible cyclic codes, and some extended binary Goppa codes. In particular, the second generalized Hamming weight of primitive double-error-correcting BCH codes is determined and upper and lower bounds are obtained for the generalized Hamming weights for the codes studied. These bounds are compared to results from other methods

Keywords

cryptography; error correction codes; binary Goppa codes; binary cyclic codes; cryptographical applications; cyclic cods; double-error-correcting BCH codes; fundamental code parameters; generalized Hamming weights; linear code; lower bounds; minimal overlap structures; reversible cyclic codes; subcodes; triple-error-correcting BCH codes; upper bounds; Computer science; Cryptography; Hamming distance; Hamming weight; Information theory; Linear code; Protection;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.135653

Filename

135653