A recursive construction for projective Reed-Muller codes
Information Theory
2024-11-12 v2 Commutative Algebra
math.IT
Abstract
We give a recursive construction for projective Reed-Muller codes in terms of affine Reed-Muller codes and projective Reed-Muller codes in fewer variables. From this construction, we obtain the dimension of the subfield subcodes of projective Reed-Muller codes for some particular degrees that give codes with good parameters. Moreover, from this recursive construction we derive a lower bound for the generalized Hamming weights of projective Reed-Muller codes which is sharp in most of the cases we have checked.
Cite
@article{arxiv.2312.05072,
title = {A recursive construction for projective Reed-Muller codes},
author = {Rodrigo San-José},
journal= {arXiv preprint arXiv:2312.05072},
year = {2024}
}