Information on Result #661401
Linear OA(16128, 560, F16, 53) (dual of [560, 432, 54]-code), using trace code based on linear OA(25664, 280, F256, 53) (dual of [280, 216, 54]-code), using
- construction X applied to AG(F, Q+100P) ⊂ AG(F, Q+106P) [i] based on
- linear OA(25653, 257, F256, 53) (dual of [257, 204, 54]-code or 257-arc in PG(52,256)), using algebraic-geometric code AG(F, Q+100P) 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(25641, 257, F256, 41) (dual of [257, 216, 42]-code or 257-arc in PG(40,256)), using algebraic-geometric code AG(F, Q+106P) 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(25611, 23, F256, 11) (dual of [23, 12, 12]-code or 23-arc in PG(10,256)), using
- discarding factors / shortening the dual code based on linear OA(25611, 256, F256, 11) (dual of [256, 245, 12]-code or 256-arc in PG(10,256)), using
- Reed–Solomon code RS(245,256) [i]
- discarding factors / shortening the dual code based on linear OA(25611, 256, F256, 11) (dual of [256, 245, 12]-code or 256-arc in PG(10,256)), 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(16129, 561, F16, 53) (dual of [561, 432, 54]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(16130, 562, F16, 53) (dual of [562, 432, 54]-code) | [i] | ||
| 3 | Linear OOA(16128, 280, F16, 2, 53) (dual of [(280, 2), 432, 54]-NRT-code) | [i] | OOA Folding | |