Information on Result #1821055
OA(12824, 260, S128, 20), using discarding parts of the base based on linear OA(25621, 260, F256, 20) (dual of [260, 239, 21]-code), using
- construction X applied to AG(F,118P) ⊂ AG(F,119P) [i] based on
- linear OA(25620, 257, F256, 20) (dual of [257, 237, 21]-code or 257-arc in PG(19,256)), using algebraic-geometric code AG(F,118P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using the rational function field F256(x) [i]
- linear OA(25618, 257, F256, 18) (dual of [257, 239, 19]-code or 257-arc in PG(17,256)), using algebraic-geometric code AG(F,119P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2561, 3, F256, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Constructive.
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 | OA(12825, 261, S128, 20) | [i] | Code Embedding in Larger Space | |
| 2 | OA(12826, 262, S128, 20) | [i] | ||
| 3 | OA(12874, 548, S128, 41) | [i] | (u, u+v)-Construction | |
| 4 | OA(12875, 550, S128, 41) | [i] | ||
| 5 | OA(12876, 552, S128, 41) | [i] | ||
| 6 | OA(12877, 554, S128, 41) | [i] | ||
| 7 | OA(12873, 548, S128, 40) | [i] | ||
| 8 | OA(12874, 550, S128, 40) | [i] | ||
| 9 | OA(12875, 552, S128, 40) | [i] | ||