Information on Result #1475521
Linear OOA(25668, 1028, F256, 2, 40) (dual of [(1028, 2), 1988, 41]-NRT-code), using construction X applied to AG(2;F,2007P) ⊂ AG(2;F,2012P) based on
- linear OOA(25664, 1024, F256, 2, 40) (dual of [(1024, 2), 1984, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,2007P) [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
- K1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- linear OOA(25659, 1024, F256, 2, 35) (dual of [(1024, 2), 1989, 36]-NRT-code), using algebraic-geometric NRT-code AG(2;F,2012P) [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025 (see above)
- linear OOA(2564, 4, F256, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2564, 256, F256, 2, 4) (dual of [(256, 2), 508, 5]-NRT-code), using
- Reed–Solomon NRT-code RS(2;508,256) [i]
- discarding factors / shortening the dual code based on linear OOA(2564, 256, F256, 2, 4) (dual of [(256, 2), 508, 5]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(25668, 1028, F256, 3, 40) (dual of [(1028, 3), 3016, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25668, 1028, F256, 4, 40) (dual of [(1028, 4), 4044, 41]-NRT-code) | [i] | ||
| 3 | Linear OOA(25668, 1028, F256, 5, 40) (dual of [(1028, 5), 5072, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(25668, 1028, F256, 6, 40) (dual of [(1028, 6), 6100, 41]-NRT-code) | [i] | ||
| 5 | Digital (28, 68, 1028)-net over F256 | [i] | ||