Work

On the minimum distance, minimum weight codewords, and the dimension of projective Reed-Muller codes

Year: 2023

Type: article

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.

Source: Advances in Mathematics of Communications

DOI: 10.3934/amc.2023035

Authors: Sudhir R. Ghorpade, Rati Ludhani

Institution: Indian Institute of Technology Bombay

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: Department of Science and Technology, Ministry of Science and Technology, India, Indian Institute of Technology Bombay, Russian Science Foundation

Awards: G5290991619, G744970817, G8195357926