Information on Result #644845
Linear OA(1622, 69, F16, 14) (dual of [69, 47, 15]-code), using construction X applied to AG(F,49P) ⊂ AG(F,52P) based on
- 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, using
- the Hermitian function field over F16 [i]
- linear OA(1617, 64, F16, 11) (dual of [64, 47, 12]-code), using algebraic-geometric code AG(F,52P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(162, 5, F16, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), 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(1680, 583, F16, 29) (dual of [583, 503, 30]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(16104, 4165, F16, 29) (dual of [4165, 4061, 30]-code) | [i] | ||
| 3 | Linear OA(16101, 4165, F16, 28) (dual of [4165, 4064, 29]-code) | [i] | ||
| 4 | Linear OA(16104, 4168, F16, 29) (dual of [4168, 4064, 30]-code) | [i] | ||
| 5 | Linear OA(16105, 4172, F16, 29) (dual of [4172, 4067, 30]-code) | [i] | ||
| 6 | Linear OA(16101, 4168, F16, 28) (dual of [4168, 4067, 29]-code) | [i] | ||
| 7 | Linear OOA(1622, 34, F16, 2, 14) (dual of [(34, 2), 46, 15]-NRT-code) | [i] | OOA Folding | |