Information on Result #657418
Linear OA(4919, 57, F49, 16) (dual of [57, 38, 17]-code), using construction X applied to AG(F, Q+15P) ⊂ AG(F, Q+17P) based on
- linear OA(4916, 50, F49, 16) (dual of [50, 34, 17]-code or 50-arc in PG(15,49)), using algebraic-geometric code AG(F, Q+15P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using the rational function field F49(x) [i]
- linear OA(4912, 50, F49, 12) (dual of [50, 38, 13]-code or 50-arc in PG(11,49)), using algebraic-geometric code AG(F, Q+17P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- linear OA(493, 7, F49, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,49) or 7-cap in PG(2,49)), using
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- Reed–Solomon code RS(46,49) [i]
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), 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(738, 114, F7, 16) (dual of [114, 76, 17]-code) | [i] | Trace Code | |