Information on Result #657207
Linear OA(2510, 31, F25, 8) (dual of [31, 21, 9]-code), using construction X applied to AG(F, Q+5P) ⊂ AG(F, Q+6P) based on
- 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, using the rational function field F25(x) [i]
- linear OA(255, 26, F25, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using algebraic-geometric code AG(F,10P) with 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(2543, 657, F25, 17) (dual of [657, 614, 18]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2559, 15657, F25, 17) (dual of [15657, 15598, 18]-code) | [i] | ||
| 3 | Linear OA(2575, 390657, F25, 17) (dual of [390657, 390582, 18]-code) | [i] | ||
| 4 | Linear OA(2541, 656, F25, 16) (dual of [656, 615, 17]-code) | [i] | ||
| 5 | Linear OA(2556, 15656, F25, 16) (dual of [15656, 15600, 17]-code) | [i] | ||
| 6 | Linear OA(2571, 390656, F25, 16) (dual of [390656, 390585, 17]-code) | [i] | ||
| 7 | Linear OA(2543, 659, F25, 17) (dual of [659, 616, 18]-code) | [i] | ||
| 8 | Linear OA(2541, 659, F25, 16) (dual of [659, 618, 17]-code) | [i] | ||
| 9 | Linear OA(25109, 659, F25, 48) (dual of [659, 550, 49]-code) | [i] | Construction XX with a Chain of Cyclic Codes | |
| 10 | Linear OA(25105, 659, F25, 46) (dual of [659, 554, 47]-code) | [i] | ||
| 11 | Linear OA(25101, 659, F25, 44) (dual of [659, 558, 45]-code) | [i] | ||
| 12 | Linear OA(2597, 659, F25, 42) (dual of [659, 562, 43]-code) | [i] | ||
| 13 | Linear OA(2593, 659, F25, 40) (dual of [659, 566, 41]-code) | [i] | ||
| 14 | Linear OA(2589, 659, F25, 38) (dual of [659, 570, 39]-code) | [i] | ||
| 15 | Linear OA(2585, 659, F25, 36) (dual of [659, 574, 37]-code) | [i] | ||
| 16 | Linear OA(2581, 659, F25, 34) (dual of [659, 578, 35]-code) | [i] | ||
| 17 | Linear OA(2577, 659, F25, 32) (dual of [659, 582, 33]-code) | [i] | ||
| 18 | Linear OA(2573, 659, F25, 30) (dual of [659, 586, 31]-code) | [i] | ||
| 19 | Linear OA(2561, 659, F25, 24) (dual of [659, 598, 25]-code) | [i] | ||