Structure of weighted projective Reed-Muller codes
Information Theory
2026-03-26 v1 Commutative Algebra
math.IT
Abstract
We provide a comprehensive overview of the fundamental structural properties of weighted projective Reed-Muller codes. We give a recursive construction for these codes, under some conditions for the weights, and we use it to derive bounds on the generalized Hamming weights and to obtain a recursive construction for their subfield subcodes and their dual codes. The dual codes are further studied in more generality, where the recursive constructions may not apply, obtaining a description as an evaluation code when the degree is low. We also provide insights into the Schur products of these codes when they are not degenerate.
Cite
@article{arxiv.2603.24397,
title = {Structure of weighted projective Reed-Muller codes},
author = {Jade Nardi and Rodrigo San-José},
journal= {arXiv preprint arXiv:2603.24397},
year = {2026}
}