Information on Result #661208
Linear OA(1688, 528, F16, 41) (dual of [528, 440, 42]-code), using trace code based on linear OA(25644, 264, F256, 41) (dual of [264, 220, 42]-code), using
- construction X applied to AG(F, Q+106P) ⊂ AG(F, Q+108P) [i] based on
- linear OA(25641, 257, F256, 41) (dual of [257, 216, 42]-code or 257-arc in PG(40,256)), using algebraic-geometric code AG(F, Q+106P) 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(25637, 257, F256, 37) (dual of [257, 220, 38]-code or 257-arc in PG(36,256)), using algebraic-geometric code AG(F, Q+108P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2563, 7, F256, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,256) or 7-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), 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 | Linear OA(1689, 529, F16, 41) (dual of [529, 440, 42]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1688, 264, F16, 2, 41) (dual of [(264, 2), 440, 42]-NRT-code) | [i] | OOA Folding | |