Information on Result #657388
Linear OA(4917, 53, F49, 16) (dual of [53, 36, 17]-code), using construction X applied to AG(F, Q+15P) ⊂ AG(F, Q+16P) 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(4914, 50, F49, 14) (dual of [50, 36, 15]-code or 50-arc in PG(13,49)), using algebraic-geometric code AG(F, Q+16P) 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(491, 3, F49, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(734, 106, F7, 16) (dual of [106, 72, 17]-code) | [i] | Trace Code | |
| 2 | Linear OA(4951, 106, F49, 33) (dual of [106, 55, 34]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4952, 108, F49, 33) (dual of [108, 56, 34]-code) | [i] | ||
| 4 | Linear OA(4950, 106, F49, 32) (dual of [106, 56, 33]-code) | [i] | ||
| 5 | Linear OA(4951, 108, F49, 32) (dual of [108, 57, 33]-code) | [i] | ||
| 6 | Linear OA(4925, 103, F49, 16) (dual of [103, 78, 17]-code) | [i] | ||
| 7 | Linear OA(4926, 106, F49, 16) (dual of [106, 80, 17]-code) | [i] | ||