Information on Result #658627
Linear OA(1669, 78, F16, 58) (dual of [78, 9, 59]-code), using construction X applied to AG(F,5P) ⊂ AG(F,14P) based on
- linear OA(1661, 64, F16, 58) (dual of [64, 3, 59]-code), using algebraic-geometric code AG(F,5P) 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(168, 14, F16, 8) (dual of [14, 6, 9]-code or 14-arc in PG(7,16)), using
- discarding factors / shortening the dual code based on linear OA(168, 16, F16, 8) (dual of [16, 8, 9]-code or 16-arc in PG(7,16)), using
- Reed–Solomon code RS(8,16) [i]
- discarding factors / shortening the dual code based on linear OA(168, 16, F16, 8) (dual of [16, 8, 9]-code or 16-arc in PG(7,16)), 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(1668, 77, F16, 57) (dual of [77, 9, 58]-code) | [i] | Truncation | |
| 2 | Linear OA(1667, 76, F16, 56) (dual of [76, 9, 57]-code) | [i] | ||
| 3 | Linear OOA(1669, 39, F16, 2, 58) (dual of [(39, 2), 9, 59]-NRT-code) | [i] | OOA Folding | |