Information on Result #1303825
Linear OA(16123, 1028, F16, 53) (dual of [1028, 905, 54]-code), using construction X with Varšamov bound based on
- linear OA(16122, 1026, F16, 53) (dual of [1026, 904, 54]-code), using
- trace code [i] based on linear OA(25661, 513, F256, 53) (dual of [513, 452, 54]-code), using
- extended algebraic-geometric code AGe(F,459P) [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,459P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25661, 513, F256, 53) (dual of [513, 452, 54]-code), using
- linear OA(16122, 1027, F16, 52) (dual of [1027, 905, 53]-code), using Gilbert–Varšamov bound and bm = 16122 > Vbs−1(k−1) = 647 541201 260657 039266 468286 788610 074332 352670 314324 999940 023904 646285 207970 657811 077217 014724 852149 279455 750443 066309 142089 083545 740416 644972 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(16123, 980, F16, 2, 53) (dual of [(980, 2), 1837, 54]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OA(16124, 1041, F16, 53) (dual of [1041, 917, 54]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(16125, 1085, F16, 53) (dual of [1085, 960, 54]-code) | [i] | ||