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

被引：0

作者：

Ghorpade, Sudhir R. ^{[1
]}

Ludhani, Rati ^{[1
]}

机构：

[1] Indian Inst Technol, Dept Math, Mumbai 400076, India

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2024年 / 18卷 / 02期

关键词：

Linear code; dimension; minimum distance; minimum weight code-word; Reed-Muller code; projective Reed-Muller code; Gaussian binomial coefficient; GENERALIZED HAMMING WEIGHTS; AFFINE;

D O I：

10.3934/amc.2023035

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

. 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.

引用

页码：360 / 382

页数：23

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