Information on Result #671998
Linear OA(4939, 2502, F49, 15) (dual of [2502, 2463, 16]-code), using (u, u+v)-construction based on
- linear OA(4910, 100, F49, 7) (dual of [100, 90, 8]-code), using
- (u, u+v)-construction [i] 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(497, 50, F49, 7) (dual of [50, 43, 8]-code or 50-arc in PG(6,49)), using
- extended Reed–Solomon code RSe(43,49) [i]
- the expurgated narrow-sense BCH-code C(I) with length 50 | 492−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- 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)
- algebraic-geometric code AG(F,14P) with degPÂ =Â 3 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- algebraic-geometric code AG(F, Q+8P) with degQ = 2 and degPÂ =Â 5 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- 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
- (u, u+v)-construction [i] based on
- linear OA(4929, 2402, F49, 15) (dual of [2402, 2373, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
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(4939, 1251, F49, 2, 15) (dual of [(1251, 2), 2463, 16]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4939, 834, F49, 3, 15) (dual of [(834, 3), 2463, 16]-NRT-code) | [i] | ||