Information on Result #657151
Linear OA(2513, 26, F25, 13) (dual of [26, 13, 14]-code or 26-arc in PG(12,25)), using algebraic-geometric code AG(F,6P) with degPÂ =Â 2 based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
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
- Extended Reed–Solomon Code [i]
- Expurgated Narrow-Sense BCH-Codes (BCH-Bound) [i]
- Algebraic-Geometric Codes Defined Using a Non-Rational Place [i]
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(526, 52, F5, 13) (dual of [52, 26, 14]-code) | [i] | Trace Code | |
| 2 | Linear OA(2563, 651, F25, 27) (dual of [651, 588, 28]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(2589, 15651, F25, 27) (dual of [15651, 15562, 28]-code) | [i] | ||
| 4 | Linear OA(2562, 651, F25, 26) (dual of [651, 589, 27]-code) | [i] | ||
| 5 | Linear OA(2586, 15651, F25, 26) (dual of [15651, 15565, 27]-code) | [i] | ||
| 6 | Linear OA(25110, 390651, F25, 26) (dual of [390651, 390541, 27]-code) | [i] | ||
| 7 | Linear OA(552, 78, F5, 27) (dual of [78, 26, 28]-code) | [i] | Concatenation of Two Codes | |
| 8 | Linear OA(2516, 29, F25, 15) (dual of [29, 13, 16]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 9 | Linear OA(2514, 29, F25, 13) (dual of [29, 15, 14]-code) | [i] | ✔ | |
| 10 | Linear OA(2518, 31, F25, 16) (dual of [31, 13, 17]-code) | [i] | ✔ | |
| 11 | Linear OA(2515, 31, F25, 13) (dual of [31, 16, 14]-code) | [i] | ✔ | |
| 12 | Linear OA(2572, 677, F25, 27) (dual of [677, 605, 28]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 13 | Linear OA(2598, 15677, F25, 27) (dual of [15677, 15579, 28]-code) | [i] | ||
| 14 | Linear OA(2570, 677, F25, 26) (dual of [677, 607, 27]-code) | [i] | ||
| 15 | Linear OA(2594, 15677, F25, 26) (dual of [15677, 15583, 27]-code) | [i] | ||
| 16 | Linear OA(2531, 907, F25, 13) (dual of [907, 876, 14]-code) | [i] | Varšamov–Edel Lengthening | |