Relative Generalized Hamming weights of affine Cartesian codes
Mrinmoy Datta
TL;DR
This paper explicitly determines all the relative generalized Hamming weights of affine Cartesian codes, extending previous results on Reed-Muller and affine Cartesian codes using footprints and combinatorics.
Contribution
It provides a complete characterization of the relative generalized Hamming weights for affine Cartesian codes, generalizing prior work on related codes.
Findings
Explicit formulas for all relative generalized Hamming weights
Extension of previous results on Reed-Muller codes
Use of footprints and extremal combinatorics techniques
Abstract
We explicitly determine all the relative generalized Hamming weights of affine Cartesian codes using the notion of footprints and results from extremal combinatorics. This generalizes the previous works on the determination of relative generalized Hamming weights of Reed-Muller codes by Geil and Martin, as well as the determination of all the generalized Hamming weights of the affine Cartesian codes by Beelen and Datta.
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