Information on Result #658606
Linear OA(1661, 68, F16, 54) (dual of [68, 7, 55]-code), using construction X applied to AG(F,9P) ⊂ AG(F,12P) based on
- linear OA(1659, 64, F16, 54) (dual of [64, 5, 55]-code), using algebraic-geometric code AG(F,9P) 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(1657, 64, F16, 51) (dual of [64, 7, 52]-code), using algebraic-geometric code AG(F,12P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(162, 4, F16, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), 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(16129, 136, F16, 109) (dual of [136, 7, 110]-code) | [i] | Repeating Each Code Word | |
| 2 | Linear OA(16127, 134, F16, 108) (dual of [134, 7, 109]-code) | [i] | Juxtaposition | |
| 3 | Linear OOA(1661, 34, F16, 2, 54) (dual of [(34, 2), 7, 55]-NRT-code) | [i] | OOA Folding | |