Information on Result #734518
Linear OA(4945, 2456, F49, 18) (dual of [2456, 2411, 19]-code), using (u, u+v)-construction based on
- linear OA(4910, 53, F49, 9) (dual of [53, 43, 10]-code), using
- construction X applied to AG(F,20P) ⊂ AG(F,21P) [i] based on
- linear OA(499, 50, F49, 9) (dual of [50, 41, 10]-code or 50-arc in PG(8,49)), using algebraic-geometric code AG(F,20P) 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(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 (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
- construction X applied to AG(F,20P) ⊂ AG(F,21P) [i] based on
- linear OA(4935, 2403, F49, 18) (dual of [2403, 2368, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(4935, 2401, F49, 18) (dual of [2401, 2366, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(4933, 2401, F49, 17) (dual of [2401, 2368, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(17) ⊂ Ce(16) [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(4945, 1228, F49, 2, 18) (dual of [(1228, 2), 2411, 19]-NRT-code) | [i] | OOA Folding | |