Information on Result #659018
Linear OA(16124, 142, F16, 89) (dual of [142, 18, 90]-code), using repeating each code word 2 times based on linear OA(1653, 71, F16, 44) (dual of [71, 18, 45]-code), using
- construction X applied to AG(F,19P) ⊂ AG(F,23P) [i] based on
- linear OA(1650, 64, F16, 44) (dual of [64, 14, 45]-code), using algebraic-geometric code AG(F,19P) [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(1646, 64, F16, 40) (dual of [64, 18, 41]-code), using algebraic-geometric code AG(F,23P) [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
- linear OA(1650, 64, F16, 44) (dual of [64, 14, 45]-code), using algebraic-geometric code AG(F,19P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, 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(16124, 142, F16, 88) (dual of [142, 18, 89]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(16123, 141, F16, 88) (dual of [141, 18, 89]-code) | [i] | Truncation | |
| 3 | Linear OOA(16124, 71, F16, 2, 89) (dual of [(71, 2), 18, 90]-NRT-code) | [i] | OOA Folding | |