Information on Result #661198
Linear OA(1686, 532, F16, 39) (dual of [532, 446, 40]-code), using trace code based on linear OA(25643, 266, F256, 39) (dual of [266, 223, 40]-code), using
- construction X applied to AG(F, Q+43P) ⊂ AG(F, Q+44P) [i] based on
- linear OA(25639, 257, F256, 39) (dual of [257, 218, 40]-code or 257-arc in PG(38,256)), using algebraic-geometric code AG(F, Q+107P) with degQ = 3 and 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(25634, 257, F256, 34) (dual of [257, 223, 35]-code or 257-arc in PG(33,256)), using algebraic-geometric code AG(F,111P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2564, 9, F256, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), 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(1687, 533, F16, 39) (dual of [533, 446, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1686, 266, F16, 2, 39) (dual of [(266, 2), 446, 40]-NRT-code) | [i] | OOA Folding | |