Generalized Reed-Muller codes: A new construction of information sets
Information Theory
2024-01-31 v1 math.IT
Abstract
In [2] we show how to construct information sets for Reed-Muller codes only in terms of their basic parameters. In this work we deal with the corresponding problem for q-ary Generalized Reed-Muller codes of first and second order. We see that for first-order codes the result for binary Reed-Muller codes is also valid, while for second-order codes, with q > 2, we have to manage more complex defining sets and we show that we get different information sets. We also present some examples and associated open problems.
Keywords
Cite
@article{arxiv.2401.16911,
title = {Generalized Reed-Muller codes: A new construction of information sets},
author = {José Joaquín Bernal},
journal= {arXiv preprint arXiv:2401.16911},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2401.10109