Information on Result #658613
Linear OA(1661, 70, F16, 53) (dual of [70, 9, 54]-code), using construction X applied to AG(F,10P) ⊂ AG(F,14P) 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(1655, 64, F16, 49) (dual of [64, 9, 50]-code), using algebraic-geometric code AG(F,14P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(163, 6, F16, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,16) or 6-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(16126, 135, F16, 104) (dual of [135, 9, 105]-code) | [i] | Juxtaposition | |
| 2 | Linear OOA(1661, 35, F16, 2, 53) (dual of [(35, 2), 9, 54]-NRT-code) | [i] | OOA Folding | |