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.
| Original language | English |
|---|---|
| Pages (from-to) | 360-382 |
| Number of pages | 23 |
| Journal | Advances in Mathematics of Communications |
| Volume | 18 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Apr 2024 |
| Externally published | Yes |
Keywords
- Gaussian binomial coefficient
- Linear code
- Reed-Muller code
- dimension
- minimum distance
- minimum weight codeword
- projective Reed-Muller code
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