Information on Result #661222
Linear OA(1692, 548, F16, 38) (dual of [548, 456, 39]-code), using trace code based on linear OA(25646, 274, F256, 38) (dual of [274, 228, 39]-code), using
- construction X applied to AG(F, Q+72P) ⊂ AG(F, Q+75P) [i] based on
- linear OA(25638, 257, F256, 38) (dual of [257, 219, 39]-code or 257-arc in PG(37,256)), using algebraic-geometric code AG(F,109P) 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(25629, 257, F256, 29) (dual of [257, 228, 30]-code or 257-arc in PG(28,256)), using algebraic-geometric code AG(F, Q+112P) 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(2568, 17, F256, 8) (dual of [17, 9, 9]-code or 17-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), 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(1693, 549, F16, 38) (dual of [549, 456, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1692, 274, F16, 2, 38) (dual of [(274, 2), 456, 39]-NRT-code) | [i] | OOA Folding | |