Information on Result #658619
Linear OA(1662, 72, F16, 53) (dual of [72, 10, 54]-code), using construction X applied to AG(F,10P) ⊂ AG(F,15P) based on
- linear OA(1658, 64, F16, 53) (dual of [64, 6, 54]-code), using algebraic-geometric code AG(F,10P) with known gap numbers [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(1654, 64, F16, 48) (dual of [64, 10, 49]-code), using algebraic-geometric code AG(F,15P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(164, 8, F16, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,16)), using
- discarding factors / shortening the dual code based on linear OA(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), using
- Reed–Solomon code RS(12,16) [i]
- discarding factors / shortening the dual code based on linear OA(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), 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(16126, 136, F16, 102) (dual of [136, 10, 103]-code) | [i] | Juxtaposition | |
| 2 | Linear OA(16127, 137, F16, 103) (dual of [137, 10, 104]-code) | [i] | ||
| 3 | Linear OOA(1662, 36, F16, 2, 53) (dual of [(36, 2), 10, 54]-NRT-code) | [i] | OOA Folding | |