Information on Result #657398
Linear OA(497, 53, F49, 6) (dual of [53, 46, 7]-code), using construction X applied to AG(F, Q+20P) ⊂ AG(F, Q+21P) based on
- linear OA(496, 50, F49, 6) (dual of [50, 44, 7]-code or 50-arc in PG(5,49)), using algebraic-geometric code AG(F, Q+20P) 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 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)
- 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
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 OA(714, 106, F7, 6) (dual of [106, 92, 7]-code) | [i] | Trace Code | |
| 2 | Linear OA(4932, 2455, F49, 13) (dual of [2455, 2423, 14]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4944, 117703, F49, 13) (dual of [117703, 117659, 14]-code) | [i] | ||
| 4 | Linear OA(4930, 2454, F49, 12) (dual of [2454, 2424, 13]-code) | [i] | ||
| 5 | Linear OA(4941, 117702, F49, 12) (dual of [117702, 117661, 13]-code) | [i] | ||
| 6 | Linear OA(4952, 5764854, F49, 12) (dual of [5764854, 5764802, 13]-code) | [i] | ||
| 7 | Linear OA(4932, 2456, F49, 13) (dual of [2456, 2424, 14]-code) | [i] | ||
| 8 | Linear OA(4933, 2460, F49, 13) (dual of [2460, 2427, 14]-code) | [i] | ||
| 9 | Linear OA(4944, 117705, F49, 13) (dual of [117705, 117661, 14]-code) | [i] | ||
| 10 | Linear OA(4945, 117710, F49, 13) (dual of [117710, 117665, 14]-code) | [i] | ||
| 11 | Linear OA(4930, 2456, F49, 12) (dual of [2456, 2426, 13]-code) | [i] | ||
| 12 | Linear OA(4931, 2459, F49, 12) (dual of [2459, 2428, 13]-code) | [i] | ||
| 13 | Linear OA(4941, 117705, F49, 12) (dual of [117705, 117664, 13]-code) | [i] | ||
| 14 | Linear OA(4942, 117709, F49, 12) (dual of [117709, 117667, 13]-code) | [i] | ||
| 15 | Linear OA(4952, 5764858, F49, 12) (dual of [5764858, 5764806, 13]-code) | [i] | ||
| 16 | Linear OA(4953, 5764863, F49, 12) (dual of [5764863, 5764810, 13]-code) | [i] | ||
| 17 | Linear OA(4948, 117753, F49, 13) (dual of [117753, 117705, 14]-code) | [i] | (u, u−v, u+v+w)-Construction | |