ON THE MINIMUM DISTANCE, MINIMUM WEIGHT CODEWORDS, AND THE DIMENSION OF PROJECTIVE REED-MULLER CODES

Sudhir R. Ghorpade; Rati Ludhani

doi:10.3934/amc.2023035

ON THE MINIMUM DISTANCE, MINIMUM WEIGHT CODEWORDS, AND THE DIMENSION OF PROJECTIVE REED-MULLER CODES

Sudhir R. Ghorpade
, Rati Ludhani

Department of Mathematics
Indian Institute of Technology Bombay

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

11 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	360-382
Nombre de pages	23
journal	Advances in Mathematics of Communications
Volume	18
Numéro de publication	2
Les DOIs	https://doi.org/10.3934/amc.2023035
état	Publié - 1 avr. 2024
Modification externe	Oui

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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 = "Gaussian binomial coefficient, Linear code, Reed-Muller code, dimension, minimum distance, minimum weight codeword, projective Reed-Muller code",

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KW - Linear code

KW - Reed-Muller code

KW - dimension

KW - minimum distance

KW - minimum weight codeword

KW - projective Reed-Muller code

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ON THE MINIMUM DISTANCE, MINIMUM WEIGHT CODEWORDS, AND THE DIMENSION OF PROJECTIVE REED-MULLER CODES

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