On the Minimum Distance, Minimum Weight Codewords, and the Dimension of Projective Reed-Muller Codes
Information Theory
2023-09-29 v2 Combinatorics
math.IT
Abstract
We give an alternative proof of the formula for the minimum distance of a projective Reed-Muller code of an arbitrary order. It leads to a complete characterization of the minimum weight codewords of a projective Reed-Muller code. This is then used to determine the number of minimum weight codewords of a projective Reed-Muller code. Various formulas for the dimension of a projective Reed-Muller code, and their equivalences are also discussed.
Keywords
Cite
@article{arxiv.2309.10196,
title = {On the Minimum Distance, Minimum Weight Codewords, and the Dimension of Projective Reed-Muller Codes},
author = {Sudhir R. Ghorpade and Rati Ludhani},
journal= {arXiv preprint arXiv:2309.10196},
year = {2023}
}
Comments
24 pages; to appear in Adv. Math. Commun.; some typos corrected and a reference added in this version