Information on Result #655611
Linear OA(8171, 378, F81, 51) (dual of [378, 307, 52]-code), using construction X applied to AG(F,317P) ⊂ AG(F,322P) based on
- linear OA(8167, 369, F81, 51) (dual of [369, 302, 52]-code), using algebraic-geometric code AG(F,317P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- linear OA(8162, 369, F81, 46) (dual of [369, 307, 47]-code), using algebraic-geometric code AG(F,322P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370 (see above)
- linear OA(814, 9, F81, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,81)), using
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), using
- Reed–Solomon code RS(77,81) [i]
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), 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(9142, 756, F9, 51) (dual of [756, 614, 52]-code) | [i] | Trace Code | |
| 2 | OA(2795, 378, S27, 51) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(8171, 189, F81, 2, 51) (dual of [(189, 2), 307, 52]-NRT-code) | [i] | OOA Folding | |