Information on Result #657205
Linear OA(2513, 31, F25, 11) (dual of [31, 18, 12]-code), using construction X applied to AG(F, Q+4P) ⊂ AG(F, Q+5P) based on
- linear OA(2511, 26, F25, 11) (dual of [26, 15, 12]-code or 26-arc in PG(10,25)), using algebraic-geometric code AG(F,7P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- linear OA(258, 26, F25, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,25)), using algebraic-geometric code AG(F, Q+7P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(252, 5, F25, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), 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(2558, 657, F25, 23) (dual of [657, 599, 24]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2580, 15657, F25, 23) (dual of [15657, 15577, 24]-code) | [i] | ||
| 3 | Linear OA(25102, 390657, F25, 23) (dual of [390657, 390555, 24]-code) | [i] | ||
| 4 | Linear OA(2556, 656, F25, 22) (dual of [656, 600, 23]-code) | [i] | ||
| 5 | Linear OA(2577, 15656, F25, 22) (dual of [15656, 15579, 23]-code) | [i] | ||
| 6 | Linear OA(2598, 390656, F25, 22) (dual of [390656, 390558, 23]-code) | [i] | ||
| 7 | Linear OA(2588, 15686, F25, 23) (dual of [15686, 15598, 24]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 8 | Linear OA(25110, 390686, F25, 23) (dual of [390686, 390576, 24]-code) | [i] | ||
| 9 | Linear OA(25110, 657, F25, 51) (dual of [657, 547, 52]-code) | [i] | Construction X with Cyclic Codes | |
| 10 | Linear OA(2589, 680, F25, 36) (dual of [680, 591, 37]-code) | [i] | Construction XX with Cyclic Codes | |
| 11 | Linear OA(2589, 681, F25, 36) (dual of [681, 592, 37]-code) | [i] | ||
| 12 | Linear OA(2591, 680, F25, 37) (dual of [680, 589, 38]-code) | [i] | ||
| 13 | Linear OA(2591, 681, F25, 37) (dual of [681, 590, 38]-code) | [i] | ||
| 14 | Linear OA(2593, 680, F25, 38) (dual of [680, 587, 39]-code) | [i] | ||
| 15 | Linear OA(2593, 681, F25, 38) (dual of [681, 588, 39]-code) | [i] | ||
| 16 | Linear OA(2595, 680, F25, 39) (dual of [680, 585, 40]-code) | [i] | ||
| 17 | Linear OA(2595, 681, F25, 39) (dual of [681, 586, 40]-code) | [i] | ||
| 18 | Linear OA(2597, 680, F25, 40) (dual of [680, 583, 41]-code) | [i] | ||
| 19 | Linear OA(2597, 681, F25, 40) (dual of [681, 584, 41]-code) | [i] | ||
| 20 | Linear OA(2599, 680, F25, 41) (dual of [680, 581, 42]-code) | [i] | ||
| 21 | Linear OA(2599, 681, F25, 41) (dual of [681, 582, 42]-code) | [i] | ||
| 22 | Linear OA(25101, 680, F25, 42) (dual of [680, 579, 43]-code) | [i] | ||
| 23 | Linear OA(25101, 681, F25, 42) (dual of [681, 580, 43]-code) | [i] | ||
| 24 | Linear OA(25103, 680, F25, 43) (dual of [680, 577, 44]-code) | [i] | ||
| 25 | Linear OA(25103, 681, F25, 43) (dual of [681, 578, 44]-code) | [i] | ||
| 26 | Linear OA(25110, 656, F25, 53) (dual of [656, 546, 54]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |