Information on Result #659023
Linear OA(16127, 146, F16, 89) (dual of [146, 19, 90]-code), using repeating each code word 2 times based on linear OA(1654, 73, F16, 44) (dual of [73, 19, 45]-code), using
- construction X applied to AG(F,19P) ⊂ AG(F,24P) [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(1645, 64, F16, 39) (dual of [64, 19, 40]-code), using algebraic-geometric code AG(F,24P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(164, 9, F16, 4) (dual of [9, 5, 5]-code or 9-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
- 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(16127, 146, F16, 88) (dual of [146, 19, 89]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(16126, 145, F16, 88) (dual of [145, 19, 89]-code) | [i] | Truncation | |
| 3 | Linear OOA(16127, 73, F16, 2, 89) (dual of [(73, 2), 19, 90]-NRT-code) | [i] | OOA Folding | |