Information on Result #1821054
OA(12824, 262, S128, 19), using discarding parts of the base based on linear OA(25621, 262, F256, 19) (dual of [262, 241, 20]-code), using
- construction X applied to AG(F,79P) ⊂ AG(F,80P) [i] based on
- linear OA(25619, 257, F256, 19) (dual of [257, 238, 20]-code or 257-arc in PG(18,256)), using algebraic-geometric code AG(F, Q+117P) with degQ = 3 and 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(25616, 257, F256, 16) (dual of [257, 241, 17]-code or 257-arc in PG(15,256)), using algebraic-geometric code AG(F,120P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2562, 5, F256, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), 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, 263, S128, 19) | [i] | Code Embedding in Larger Space | |
| 2 | OA(12826, 264, S128, 19) | [i] | ||
| 3 | OA(12872, 550, S128, 39) | [i] | (u, u+v)-Construction | |
| 4 | OA(12873, 552, S128, 39) | [i] | ||
| 5 | OA(12874, 554, S128, 39) | [i] | ||
| 6 | OA(12871, 550, S128, 38) | [i] | ||