Information on Result #657755
Linear OA(25619, 260, F256, 18) (dual of [260, 241, 19]-code), using construction X applied to AG(F,119P) ⊂ AG(F,120P) based on
- linear OA(25618, 257, F256, 18) (dual of [257, 239, 19]-code or 257-arc in PG(17,256)), using algebraic-geometric code AG(F,119P) 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(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 (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(476, 1040, F4, 18) (dual of [1040, 964, 19]-code) | [i] | Trace Code | |
| 2 | Linear OA(1638, 520, F16, 18) (dual of [520, 482, 19]-code) | [i] | ||
| 3 | OA(3231, 260, S32, 18) | [i] | Discarding Parts of the Base for OAs | |
| 4 | OA(6426, 260, S64, 18) | [i] | ||
| 5 | OA(12822, 260, S128, 18) | [i] | ||
| 6 | Linear OA(25657, 520, F256, 37) (dual of [520, 463, 38]-code) | [i] | (u, u+v)-Construction | |
| 7 | Linear OA(25658, 522, F256, 37) (dual of [522, 464, 38]-code) | [i] | ||
| 8 | Linear OA(25656, 520, F256, 36) (dual of [520, 464, 37]-code) | [i] | ||
| 9 | Linear OA(25657, 522, F256, 36) (dual of [522, 465, 37]-code) | [i] | ||
| 10 | Linear OA(25628, 517, F256, 18) (dual of [517, 489, 19]-code) | [i] | ||
| 11 | Linear OA(25629, 520, F256, 18) (dual of [520, 491, 19]-code) | [i] | ||