Name
Title | ||
|---|---|---|
Further results on Goppa codes and their applications to constructing efficient binary codes |
Abstract | ||
|---|---|---|
It is shown that Goppa codes with Goppa polynomial{g(z)}^{q}have the parameters: lengthn leq q^{m} - s_{o}, number of check symbolsn - k leq m (q - 1) (deg g), and minimum distanced geq q (deg g) + 1, whereqis a prime power,mis an integer,g(z )is an arbitrary polynomial overGF(q^{m}), and so is the number of roots ofg(z)which belong toGF(q^{m}). It is also shown that all binary Goppa codes of lengthn leq 2^{m} - s_{o}satisfy the relationn - k leq m (d - 1)/2. A new class of binary codes withn leq 2^{ m} + ms _{0}, n - k leq m (deg g) + s_{0}, andd leq 2(deg g) + 1is constructed, as well as another class of binary codes with slightly different parameters. Some of those codes are proved superior to the best codes previously known. Finally, a decoding algorithm is given for the codes constructed which uses Euclid's algorithm. |
Year | DOI | Venue |
|---|---|---|
1976 | 10.1109/TIT.1976.1055610 | Information Theory, IEEE Transactions |
Keywords | Field | DocType |
Goppa codes | Integer,Discrete mathematics,Combinatorics,Polynomial,Binary code,Decoding methods,Prime power,Mathematics,Binary number | Journal |
Volume | Issue | ISSN |
22 | 5 | 0018-9448 |
Citations | PageRank | References |
25 | 5.75 | 17 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yasuo Sugiyama | 1 | 220 | 131.91 |
| Masao Kasahara | 2 | 290 | 147.60 |
| Shigeichi Hirasawa | 3 | 78 | 53.22 |
| Toshihiko Namekawa | 4 | 90 | 107.56 |