Information on Result #644886
Linear OA(1627, 71, F16, 18) (dual of [71, 44, 19]-code), using construction X applied to AG(F,45P) ⊂ AG(F,49P) based on
- linear OA(1624, 64, F16, 18) (dual of [64, 40, 19]-code), using algebraic-geometric code AG(F,45P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- linear OA(1620, 64, F16, 14) (dual of [64, 44, 15]-code), using algebraic-geometric code AG(F,49P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(163, 7, F16, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,16) or 7-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), 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(16101, 585, F16, 37) (dual of [585, 484, 38]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(16130, 4168, F16, 37) (dual of [4168, 4038, 38]-code) | [i] | ||
| 3 | Linear OA(16127, 4167, F16, 36) (dual of [4167, 4040, 37]-code) | [i] | ||
| 4 | Linear OOA(1627, 35, F16, 2, 18) (dual of [(35, 2), 43, 19]-NRT-code) | [i] | OOA Folding | |