Information on Result #655928
Linear OA(8182, 734, F81, 44) (dual of [734, 652, 45]-code), using construction X applied to AG(F,684P) ⊂ AG(F,687P) based on
- linear OA(8180, 729, F81, 44) (dual of [729, 649, 45]-code), using algebraic-geometric code AG(F,684P) [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- the Hermitian function field over F81 [i]
- linear OA(8177, 729, F81, 41) (dual of [729, 652, 42]-code), using algebraic-geometric code AG(F,687P) [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730 (see above)
- linear OA(812, 5, F81, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), 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 OOA(8182, 367, F81, 2, 44) (dual of [(367, 2), 652, 45]-NRT-code) | [i] | OOA Folding | |