Information on Result #644881
Linear OA(1632, 71, F16, 23) (dual of [71, 39, 24]-code), using construction X applied to AG(F,40P) ⊂ AG(F,44P) based on
- linear OA(1629, 64, F16, 23) (dual of [64, 35, 24]-code), using algebraic-geometric code AG(F,40P) [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(1625, 64, F16, 19) (dual of [64, 39, 20]-code), using algebraic-geometric code AG(F,44P) [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(464, 142, F4, 23) (dual of [142, 78, 24]-code) | [i] | Trace Code | |
| 2 | Linear OA(16128, 591, F16, 47) (dual of [591, 463, 48]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(16126, 591, F16, 46) (dual of [591, 465, 47]-code) | [i] | ||
| 4 | Linear OOA(1632, 35, F16, 2, 23) (dual of [(35, 2), 38, 24]-NRT-code) | [i] | OOA Folding | |