Information on Result #1046395
Linear OOA(6474, 515, F64, 3, 42) (dual of [(515, 3), 1471, 43]-NRT-code), using construction X applied to AG(3;F,1493P) ⊂ AG(3;F,1498P) based on
- linear OOA(6470, 512, F64, 3, 42) (dual of [(512, 3), 1466, 43]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1493P) [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- linear OOA(6465, 512, F64, 3, 37) (dual of [(512, 3), 1471, 38]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1498P) [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513 (see above)
- linear OOA(644, 3, F64, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(644, 64, F64, 3, 4) (dual of [(64, 3), 188, 5]-NRT-code), using
- Reed–Solomon NRT-code RS(3;188,64) [i]
- discarding factors / shortening the dual code based on linear OOA(644, 64, F64, 3, 4) (dual of [(64, 3), 188, 5]-NRT-code), 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 OOA(6474, 515, F64, 3, 41) (dual of [(515, 3), 1471, 42]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Digital (32, 74, 515)-net over F64 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |