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Generalized Hamming weights of trace codes

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2 Author(s)
Stichtenoth, H. ; Dept. of Math. & Inf., Essen Univ., Germany ; Voss, C.

Linear codes over Fp often admit a natural representation as trace codes of codes that are defined over an extension field Fpm. 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=pm-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

Published in:

Information Theory, IEEE Transactions on  (Volume:40 ,  Issue: 2 )

Date of Publication:

Mar 1994

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