Information on Result #1303829
Linear OA(16125, 1028, F16, 54) (dual of [1028, 903, 55]-code), using construction X with Varšamov bound based on
- linear OA(16124, 1026, F16, 54) (dual of [1026, 902, 55]-code), using
- trace code [i] based on linear OA(25662, 513, F256, 54) (dual of [513, 451, 55]-code), using
- extended algebraic-geometric code AGe(F,458P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- extended algebraic-geometric code AGe(F,458P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25662, 513, F256, 54) (dual of [513, 451, 55]-code), using
- linear OA(16124, 1027, F16, 53) (dual of [1027, 903, 54]-code), using Gilbert–Varšamov bound and bm = 16124 > Vbs−1(k−1) = 182134 111981 420724 348257 878194 904826 751861 179506 358632 144141 150739 989482 862846 490472 407677 553358 237271 715754 039460 097802 273160 412662 561705 707472 726016 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(16125, 977, F16, 2, 54) (dual of [(977, 2), 1829, 55]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OA(16126, 1041, F16, 54) (dual of [1041, 915, 55]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(16127, 1082, F16, 54) (dual of [1082, 955, 55]-code) | [i] | ||