Name
Title | ||
|---|---|---|
Decoding Of Projective Reed-Muller Codes By Dividing A Projective Space Into Affine Spaces |
Abstract | ||
|---|---|---|
A projective Reed-Muller (PRM) code, obtained by modifying a Reed-Muller code with respect to a projective space, is a doubly extended Reed-Solomon code when the dimension of the related projective space is equal to 1. The minimum distance and the dual code of a PRM code are known, and some decoding examples have been presented for low-dimensional projective spaces. In this study, we construct a decoding algorithm for all PRM codes by dividing a projective space into a union of affine spaces. In addition, we determine the computational complexity and the number of correctable errors of our algorithm. Finally, we compare the codeword error rate of our algorithm with that of the minimum distance decoding. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1587/transfun.E99.A.733 | IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES |
Keywords | Field | DocType |
error-correcting codes, affine variety codes, Grobner basis, Berlekamp-Massey-Sakata algorithm, discrete Fourier transform | Discrete mathematics,Blocking set,Combinatorics,Concatenated error correction code,Homography,Reed–Muller code,Linear code,Real projective line,Hyperplane,Mathematics,Projective space | Journal |
Volume | Issue | ISSN |
E99A | 3 | 0916-8508 |
Citations | PageRank | References |
0 | 0.34 | 13 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nakashima, N. | 1 | 3 | 0.81 |
| Hajime Matsui | 2 | 18 | 8.14 |