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. © 2020, The Author(s).

Mrinmoy Datta

Department of Mathematics

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Journal	Data powered by TypesetDesigns, Codes, and Cryptography
Publisher	Data powered by TypesetSpringer
ISSN	09251022