Information on Result #658614
Linear OA(1671, 76, F16, 63) (dual of [76, 5, 64]-code), using construction X applied to AG(F,0P) ⊂ AG(F,9P) based on
- linear OA(1663, 64, F16, 63) (dual of [64, 1, 64]-code or 64-arc in PG(62,16)), using algebraic-geometric code AG(F,0P) [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(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(168, 12, F16, 8) (dual of [12, 4, 9]-code or 12-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(1670, 75, F16, 62) (dual of [75, 5, 63]-code) | [i] | Truncation | |
| 2 | Linear OA(1669, 74, F16, 61) (dual of [74, 5, 62]-code) | [i] | ||
| 3 | Linear OA(1668, 73, F16, 60) (dual of [73, 5, 61]-code) | [i] | ||
| 4 | Linear OOA(1671, 38, F16, 2, 63) (dual of [(38, 2), 5, 64]-NRT-code) | [i] | OOA Folding | |