Information on Result #669199
Linear OA(4946, 2452, F49, 19) (dual of [2452, 2406, 20]-code), using (u, u+v)-construction based on
- linear OA(499, 50, F49, 9) (dual of [50, 41, 10]-code or 50-arc in PG(8,49)), using
- extended Reed–Solomon code RSe(41,49) [i]
- the expurgated narrow-sense BCH-code C(I) with length 50 | 492−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 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]
- algebraic-geometric code AG(F, Q+12P) with degQ = 4 and 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,8P) with degPÂ =Â 5 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- linear OA(4937, 2402, F49, 19) (dual of [2402, 2365, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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(4946, 1226, F49, 2, 19) (dual of [(1226, 2), 2406, 20]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4946, 817, F49, 3, 19) (dual of [(817, 3), 2405, 20]-NRT-code) | [i] | ||