Name
Abstract | ||
|---|---|---|
It is still an open challenge in coding theory how to design a systematic linear (n, k) - code C over GF(2) with maximal minimum distance d. In this study, based on matroid theory (MT), a limited class of good systematic binary linear codes (n, k, d) is constructed, where n = 2k-1 + · · · + 2k-δ and d = 2k-2 + · · · + 2k-δ-1 for k ≥ 4, 1 ≤ δ <; k. These codes are well known as special cases of codes constructed by Solomon and Stiffler (SS) back in 1960s. Furthermore, a new shortening method is presented. By shortening the optimal codes, we can design new kinds of good systematic binary linear codes with parameters n = 2k-1 + · · · + 2k-δ - 3u and d = 2k-2 + · · · + 2k-δ-1 - 2u for 2 ≤ u ≤ 4, 2 ≤ δ <; k. The advantage of MT over the original SS construction is that it has an advantage in yielding generator matrix on systematic form. In addition, the dual code C⊥ with relative high rate and optimal minimum distance can be obtained easily in this study. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1049/iet-com.2013.0671 | IET Communications |
Keywords | Field | DocType |
systematic binary linear codes,dual code,linear codes,generator matrix,matroid theory,matrix algebra,combinatorial mathematics,coding theory,optimal codes,maximal minimum distance,shortening method,ss construction,binary codes,solomon-stiffler code construction | Matroid,Discrete mathematics,Generator matrix,Mathematical theory,Binary linear codes,Coding theory,Mathematics,Dual code | Journal |
Volume | Issue | ISSN |
8 | 6 | 1751-8628 |
Citations | PageRank | References |
0 | 0.34 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Guangfu Wu | 1 | 1 | 1.04 |
| Lin Wang | 2 | 155 | 15.90 |
| Trieu-Kien Truong | 3 | 382 | 59.00 |