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arXiv · 2309.10196

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

Sudhir R. Ghorpade·Rati Ludhani
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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.

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Sudhir R. Ghorpade, Rati Ludhani. 2023-09-18. On the Minimum Distance, Minimum Weight Codewords, and the Dimension of Projective Reed-Muller Codes. https://doi.org/10.3934/amc.2023035

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