Information on Result #657194
Linear OA(259, 31, F25, 7) (dual of [31, 22, 8]-code), using construction X applied to AG(F,6P) ⊂ AG(F,7P) based on
- linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using algebraic-geometric code AG(F,9P) 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(254, 26, F25, 4) (dual of [26, 22, 5]-code or 26-arc in PG(3,25)), using algebraic-geometric code AG(F, Q+9P) 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(2538, 657, F25, 15) (dual of [657, 619, 16]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2552, 15657, F25, 15) (dual of [15657, 15605, 16]-code) | [i] | ||
| 3 | Linear OA(2566, 390657, F25, 15) (dual of [390657, 390591, 16]-code) | [i] | ||
| 4 | Linear OA(2536, 656, F25, 14) (dual of [656, 620, 15]-code) | [i] | ||
| 5 | Linear OA(2549, 15656, F25, 14) (dual of [15656, 15607, 15]-code) | [i] | ||
| 6 | Linear OA(2562, 390656, F25, 14) (dual of [390656, 390594, 15]-code) | [i] | ||
| 7 | Linear OA(2538, 659, F25, 15) (dual of [659, 621, 16]-code) | [i] | ||
| 8 | Linear OA(2552, 15659, F25, 15) (dual of [15659, 15607, 16]-code) | [i] | ||
| 9 | Linear OA(2536, 659, F25, 14) (dual of [659, 623, 15]-code) | [i] | ||
| 10 | Linear OA(2549, 15659, F25, 14) (dual of [15659, 15610, 15]-code) | [i] | ||
| 11 | Linear OA(25106, 15657, F25, 33) (dual of [15657, 15551, 34]-code) | [i] | Construction X with Cyclic Codes | |
| 12 | Linear OA(25100, 15657, F25, 31) (dual of [15657, 15557, 32]-code) | [i] | ||
| 13 | Linear OA(2594, 15657, F25, 29) (dual of [15657, 15563, 30]-code) | [i] | ||
| 14 | Linear OA(2588, 15657, F25, 27) (dual of [15657, 15569, 28]-code) | [i] | ||
| 15 | Linear OA(2582, 15657, F25, 25) (dual of [15657, 15575, 26]-code) | [i] | ||
| 16 | Linear OA(2576, 15657, F25, 23) (dual of [15657, 15581, 24]-code) | [i] | ||
| 17 | Linear OA(2570, 15657, F25, 21) (dual of [15657, 15587, 22]-code) | [i] | ||
| 18 | Linear OA(2564, 15657, F25, 19) (dual of [15657, 15593, 20]-code) | [i] | ||
| 19 | Linear OA(2558, 15657, F25, 17) (dual of [15657, 15599, 18]-code) | [i] | ||
| 20 | Linear OA(25109, 15656, F25, 35) (dual of [15656, 15547, 36]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 21 | Linear OA(25106, 15656, F25, 34) (dual of [15656, 15550, 35]-code) | [i] | ||
| 22 | Linear OA(2579, 15656, F25, 24) (dual of [15656, 15577, 25]-code) | [i] | ||
| 23 | Linear OA(2573, 15656, F25, 22) (dual of [15656, 15583, 23]-code) | [i] | ||
| 24 | Linear OA(2567, 15656, F25, 20) (dual of [15656, 15589, 21]-code) | [i] | ||
| 25 | Linear OA(2561, 15656, F25, 18) (dual of [15656, 15595, 19]-code) | [i] | ||
| 26 | Linear OA(2555, 15656, F25, 16) (dual of [15656, 15601, 17]-code) | [i] | ||
| 27 | Linear OA(25101, 15657, F25, 32) (dual of [15657, 15556, 33]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 28 | Linear OA(2598, 15657, F25, 31) (dual of [15657, 15559, 32]-code) | [i] | ||
| 29 | Linear OA(2595, 15657, F25, 30) (dual of [15657, 15562, 31]-code) | [i] | ||
| 30 | Linear OA(2592, 15657, F25, 29) (dual of [15657, 15565, 30]-code) | [i] | ||
| 31 | Linear OA(2589, 15657, F25, 28) (dual of [15657, 15568, 29]-code) | [i] | ||
| 32 | Linear OA(2586, 15657, F25, 27) (dual of [15657, 15571, 28]-code) | [i] | ||
| 33 | Linear OA(2583, 15657, F25, 26) (dual of [15657, 15574, 27]-code) | [i] | ||