Information on Result #661261
Linear OA(16100, 544, F16, 43) (dual of [544, 444, 44]-code), using trace code based on linear OA(25650, 272, F256, 43) (dual of [272, 222, 44]-code), using
- construction X applied to AG(F, Q+105P) ⊂ AG(F, Q+109P) [i] based on
- linear OA(25643, 257, F256, 43) (dual of [257, 214, 44]-code or 257-arc in PG(42,256)), using algebraic-geometric code AG(F, Q+105P) 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(25635, 257, F256, 35) (dual of [257, 222, 36]-code or 257-arc in PG(34,256)), using algebraic-geometric code AG(F, Q+109P) 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(2567, 15, F256, 7) (dual of [15, 8, 8]-code or 15-arc in PG(6,256)), using
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- Reed–Solomon code RS(249,256) [i]
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), 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(16101, 545, F16, 43) (dual of [545, 444, 44]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(16100, 272, F16, 2, 43) (dual of [(272, 2), 444, 44]-NRT-code) | [i] | OOA Folding | |