English

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