An algorithm for computing generalized Hamming weights and the Sage package GHWs

We generalize the Brouwer-Zimmermann algorithm, which is the most efficient general algorithm for computing the minimum distance of a random linear code, to the case of generalized Hamming weights. We also adapt this algorithm to compute the relative generalized Hamming weights of a nested pair of linear codes. In the package GHWs we provide an implementation of this algorithm in Sage, as well as several other utilities for working with generalized Hamming weights. With this implementation, we show that the proposed algorithm is faster than the naive approach of computing the generalized Hamming weights using the definition.

Publication Details

Journal
ArXiv.org
Published
2025-03-22
Primary Topic
Coding theory and cryptography
Type
article
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article

An algorithm for computing generalized Hamming weights and the Sage package GHWs

ArXiv.org
Coding theory and cryptography
article

An algorithm for computing generalized Hamming weights and the Sage package GHWs

article en

Abstract

We generalize the Brouwer-Zimmermann algorithm, which is the most efficient general algorithm for computing the minimum distance of a random linear code, to the case of generalized Hamming weights. We also adapt this algorithm to compute the relative generalized Hamming weights of a nested pair of linear codes. In the package GHWs we provide an implementation of this algorithm in Sage, as well as several other utilities for working with generalized Hamming weights. With this implementation, we show that the proposed algorithm is faster than the naive approach of computing the generalized Hamming weights using the definition.

ArXiv.org
Openalex Percentile: Top 73%
Coding theory and cryptography
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An algorithm for computing generalized Hamming weights and the Sage package GHWs · ArXiv.org (2025) | TGRS Research Map | TGRS