Relative generalized Hamming weights of affine Cartesian codes-Reference-Cited by-同舟云学术

Relative generalized Hamming weights of affine Cartesian codes

Published:2020-03-10 Issue:6 Volume:88 Page:1273-1284
ISSN:0925-1022
Container-title:Designs, Codes and Cryptography
language:en
Short-container-title:Des. Codes Cryptogr.

Author:

Datta Mrinmoy

Abstract

AbstractWe 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.

Funder

Norges Forskningsråd

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computer Science Applications

Link

http://link.springer.com/content/pdf/10.1007/s10623-020-00745-8.pdf

Reference21 articles.

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4. Carvalho C., Neumann V.G.L.: On the next-to-minimal weight of affine cartesian codes. Finite Fields Appl. 44, 113–134 (2017).

5. Clements G.F., Lindström B.: A generalization of a combinatorial theorem of Macaulay. J. Comb. Theory 7, 230–238 (1969).

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