Information on Result #658259
Linear OA(25618, 262, F256, 16) (dual of [262, 244, 17]-code), using construction X applied to AG(F,80P) ⊂ AG(F,81P) 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(25613, 257, F256, 13) (dual of [257, 244, 14]-code or 257-arc in PG(12,256)), using algebraic-geometric code AG(F, Q+120P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2562, 5, F256, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), 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(1636, 524, F16, 16) (dual of [524, 488, 17]-code) | [i] | Trace Code | |
| 2 | OA(3229, 262, S32, 16) | [i] | Discarding Parts of the Base for OAs | |
| 3 | OA(6424, 262, S64, 16) | [i] | ||
| 4 | OA(12821, 262, S128, 16) | [i] | ||
| 5 | Linear OA(25653, 524, F256, 33) (dual of [524, 471, 34]-code) | [i] | (u, u+v)-Construction | |
| 6 | Linear OA(25654, 526, F256, 33) (dual of [526, 472, 34]-code) | [i] | ||
| 7 | Linear OA(25652, 524, F256, 32) (dual of [524, 472, 33]-code) | [i] | ||