Information on Result #661074
Linear OA(1654, 536, F16, 22) (dual of [536, 482, 23]-code), using trace code based on linear OA(25627, 268, F256, 22) (dual of [268, 241, 23]-code), using
- construction X applied to AG(F,117P) ⊂ AG(F,120P) [i] based on
- linear OA(25622, 257, F256, 22) (dual of [257, 235, 23]-code or 257-arc in PG(21,256)), using algebraic-geometric code AG(F,117P) 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(2565, 11, F256, 5) (dual of [11, 6, 6]-code or 11-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), 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(1655, 537, F16, 22) (dual of [537, 482, 23]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1656, 538, F16, 22) (dual of [538, 482, 23]-code) | [i] | ||
| 3 | Linear OOA(1654, 268, F16, 2, 22) (dual of [(268, 2), 482, 23]-NRT-code) | [i] | OOA Folding | |