Information on Result #734568
Linear OA(4936, 2458, F49, 14) (dual of [2458, 2422, 15]-code), using (u, u+v)-construction based on
- linear OA(499, 55, F49, 7) (dual of [55, 46, 8]-code), using
- construction X applied to AG(F,14P) ⊂ AG(F,15P) [i] based on
- linear OA(497, 50, F49, 7) (dual of [50, 43, 8]-code or 50-arc in PG(6,49)), using algebraic-geometric code AG(F,21P) with 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(494, 50, F49, 4) (dual of [50, 46, 5]-code or 50-arc in PG(3,49)), using algebraic-geometric code AG(F, Q+21P) 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(492, 5, F49, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- construction X applied to AG(F,14P) ⊂ AG(F,15P) [i] based on
- linear OA(4927, 2403, F49, 14) (dual of [2403, 2376, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(4927, 2401, F49, 14) (dual of [2401, 2374, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(4925, 2401, F49, 13) (dual of [2401, 2376, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
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(4936, 1229, F49, 2, 14) (dual of [(1229, 2), 2422, 15]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4936, 819, F49, 3, 14) (dual of [(819, 3), 2421, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(4936, 351, F49, 14, 14) (dual of [(351, 14), 4878, 15]-NRT-code) | [i] | OA Folding and Stacking | |