Information on Result #669050
Linear OA(498, 2450, F49, 4) (dual of [2450, 2442, 5]-code), using generalized (u, u+v)-construction based on
- linear OA(490, 50, F49, 0) (dual of [50, 50, 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
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(491, 50, F49, 1) (dual of [50, 49, 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
- linear OA(491, 50, F49, 1) (dual of [50, 49, 2]-code) (see above)
- linear OA(492, 50, F49, 2) (dual of [50, 48, 3]-code or 50-arc in PG(1,49)), using
- extended Reed–Solomon code RSe(48,49) [i]
- Hamming code H(2,49) [i]
- algebraic-geometric code AG(F, Q+22P) with degQ = 3 and 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
- extended Reed–Solomon code RSe(46,49) [i]
- 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)
- algebraic-geometric code AG(F,15P) with degPÂ =Â 3 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
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(498, 1225, F49, 2, 4) (dual of [(1225, 2), 2442, 5]-NRT-code) | [i] | OOA Folding | |