Recursive Decoding of Projective Reed–Muller Codes
Abstract
We give a recursive decoding algorithm for projective Reed-Muller codes making use of a decoder for affine Reed-Muller codes. We determine the number of errors that can be corrected in this way, which is the current highest for decoders of projective Reed-Muller codes. We determine the degrees for which we can decode up to the error correction capability of these codes, and we compute the order of complexity of the algorithm, given by that of the chosen decoder for affine Reed-Muller codes. We also show how the decoder behaves when increasing the number of variables and the size of the field.
Fields of Study & Subjects
Coding theory and cryptography
Error Correcting Code Techniques
Cooperative Communication and Network Coding
Publication details
- Journal / source
- IEEE Transactions on Information Theory
- Volume
- 72
- Issue
- 5
- Pages
- 2769–2779
- Publication date
- 23 February 2026
- Language
- EN