Name
Abstract | ||
|---|---|---|
The binary Melas code is a cyclic code with generator polynomial ()=()() where () is a primitive polynomial of odd degree ≥5 and the ∗ denotes reciprocation. The even-weight subcode of a Melas code has generator polynomial (+1)() and parameters [2−1,2−2−2,6]. This code is lifted to and the quaternary code is shown to have parameters [2−1,2−2−2, ≥8], where denotes the minimum Lee distance. An algebraic decoding algorithm correcting all errors of Lee weight ≤3 is presented for this code. The Gray map of this quaternary code is a binary code with parameters [2−2,2−4−4, ≥8] where is the minimum Hamming distance. For =5,7 the minimum distance equals the minimum distance of the best known linear code for the given length and code size. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s12095-015-0135-8 | Cryptography and Communications |
Keywords | Field | DocType |
Melas code,Cyclic codes,Codes over,\(\mathbb {Z}_{4}\),94B15,94B35 | Discrete mathematics,Lee distance,Combinatorics,Primitive polynomial,Binary code,Polynomial code,Ternary Golay code,Cyclic code,Hamming distance,Linear code,Mathematics | Journal |
Volume | Issue | ISSN |
8 | 1 | 1936-2447 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
6 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Adel Alahmadi | 1 | 24 | 11.27 |
| hussain alhazmi | 2 | 4 | 0.81 |
| Tor Helleseth | 3 | 1389 | 215.30 |
| Rola Hijazi | 4 | 9 | 1.73 |
| Najat M. Muthana | 5 | 1 | 1.03 |
| Patrick Solé | 6 | 636 | 89.68 |