On the Minimum Distance, Minimum Weight Codewords, and the Dimension of Projective Reed-Muller Codes

Autor:	Ghorpade, Sudhir R., Ludhani, Rati
Rok vydání:	2023
Předmět:	Computer Science - Information Theory Mathematics - Combinatorics Primary: 94B05 94B27 11B65 Secondary: 14G50
Druh dokumentu:	Working Paper
DOI:	10.3934/amc.2023035
Popis:	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. Comment: 24 pages; to appear in Adv. Math. Commun.; some typos corrected and a reference added in this version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.10196 Zobrazit plný text záznamu View this record from Arxiv