Information on Result #658622
Linear OA(1668, 76, F16, 58) (dual of [76, 8, 59]-code), using construction X applied to AG(F,5P) ⊂ AG(F,13P) 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(1656, 64, F16, 50) (dual of [64, 8, 51]-code), using algebraic-geometric code AG(F,13P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(167, 12, F16, 7) (dual of [12, 5, 8]-code or 12-arc in PG(6,16)), using
- discarding factors / shortening the dual code based on linear OA(167, 16, F16, 7) (dual of [16, 9, 8]-code or 16-arc in PG(6,16)), using
- Reed–Solomon code RS(9,16) [i]
- discarding factors / shortening the dual code based on linear OA(167, 16, F16, 7) (dual of [16, 9, 8]-code or 16-arc in PG(6,16)), 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(1667, 75, F16, 57) (dual of [75, 8, 58]-code) | [i] | Truncation | |
| 2 | Linear OA(1666, 74, F16, 56) (dual of [74, 8, 57]-code) | [i] | ||
| 3 | Linear OOA(1668, 38, F16, 2, 58) (dual of [(38, 2), 8, 59]-NRT-code) | [i] | OOA Folding | |