Information on Result #656623
Linear OA(12863, 294, F128, 51) (dual of [294, 231, 52]-code), using construction X applied to AG(F,235P) ⊂ AG(F,239P) based on
- linear OA(12860, 287, F128, 51) (dual of [287, 227, 52]-code), using algebraic-geometric code AG(F,235P) [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- linear OA(12856, 287, F128, 47) (dual of [287, 231, 48]-code), using algebraic-geometric code AG(F,239P) [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288 (see above)
- linear OA(1283, 7, F128, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,128) or 7-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
Mode: Constructive and 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 | OA(6474, 294, S64, 51) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12863, 147, F128, 2, 51) (dual of [(147, 2), 231, 52]-NRT-code) | [i] | OOA Folding | |