Information on Result #656445
Linear OA(12828, 222, F128, 20) (dual of [222, 194, 21]-code), using construction X applied to AG(F,194P) ⊂ AG(F,198P) based on
- linear OA(12825, 215, F128, 20) (dual of [215, 190, 21]-code), using algebraic-geometric code AG(F,194P) [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- linear OA(12821, 215, F128, 16) (dual of [215, 194, 17]-code), using algebraic-geometric code AG(F,198P) [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216 (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(6433, 222, S64, 20) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OA(12878, 510, F128, 41) (dual of [510, 432, 42]-code) | [i] | (u, u+v)-Construction | |