Information on Result #657757
Linear OA(25617, 260, F256, 16) (dual of [260, 243, 17]-code), using construction X applied to AG(F,120P) ⊂ AG(F,121P) based on
- linear OA(25616, 257, F256, 16) (dual of [257, 241, 17]-code or 257-arc in PG(15,256)), using algebraic-geometric code AG(F,120P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using the rational function field F256(x) [i]
- linear OA(25614, 257, F256, 14) (dual of [257, 243, 15]-code or 257-arc in PG(13,256)), using algebraic-geometric code AG(F,121P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2561, 3, F256, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 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(468, 1040, F4, 16) (dual of [1040, 972, 17]-code) | [i] | Trace Code | |
| 2 | Linear OA(1634, 520, F16, 16) (dual of [520, 486, 17]-code) | [i] | ||
| 3 | OA(3228, 260, S32, 16) | [i] | Discarding Parts of the Base for OAs | |
| 4 | OA(6423, 260, S64, 16) | [i] | ||
| 5 | OA(12820, 260, S128, 16) | [i] | ||
| 6 | Linear OA(25651, 520, F256, 33) (dual of [520, 469, 34]-code) | [i] | (u, u+v)-Construction | |
| 7 | Linear OA(25652, 522, F256, 33) (dual of [522, 470, 34]-code) | [i] | ||
| 8 | Linear OA(25650, 520, F256, 32) (dual of [520, 470, 33]-code) | [i] | ||
| 9 | Linear OA(25651, 522, F256, 32) (dual of [522, 471, 33]-code) | [i] | ||
| 10 | Linear OA(25625, 517, F256, 16) (dual of [517, 492, 17]-code) | [i] | ||