Information on Result #734677
Linear OA(4928, 5764855, F49, 7) (dual of [5764855, 5764827, 8]-code), using (u, u+v)-construction based on
- linear OA(493, 50, F49, 3) (dual of [50, 47, 4]-code or 50-arc in PG(2,49) or 50-cap in PG(2,49)), using
- extended Reed–Solomon code RSe(47,49) [i]
- oval in PG(2, 49) [i]
- algebraic-geometric code AG(F, Q+14P) with degQ = 4 and degPÂ =Â 3 [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(4925, 5764805, F49, 7) (dual of [5764805, 5764780, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(4925, 5764801, F49, 7) (dual of [5764801, 5764776, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 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(6) ⊂ Ce(5) [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(4928, 5764855, F49, 2, 7) (dual of [(5764855, 2), 11529682, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4928, 5764855, F49, 3, 7) (dual of [(5764855, 3), 17294537, 8]-NRT-code) | [i] | ||
| 3 | Digital (21, 28, 5764855)-net over F49 | [i] | ||
| 4 | Linear OOA(4928, 2882427, F49, 2, 7) (dual of [(2882427, 2), 5764826, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4928, 1921618, F49, 3, 7) (dual of [(1921618, 3), 5764826, 8]-NRT-code) | [i] | ||