Information on Result #1092285
Linear OOA(8161, 373, F81, 4, 37) (dual of [(373, 4), 1431, 38]-NRT-code), using construction X applied to AG(4;F,1438P) ⊂ AG(4;F,1447P) based on
- linear OOA(8153, 369, F81, 4, 37) (dual of [(369, 4), 1423, 38]-NRT-code), using algebraic-geometric NRT-code AG(4;F,1438P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- linear OOA(8144, 369, F81, 4, 28) (dual of [(369, 4), 1432, 29]-NRT-code), using algebraic-geometric NRT-code AG(4;F,1447P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370 (see above)
- linear OOA(818, 4, F81, 4, 8) (dual of [(4, 4), 8, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(818, 81, F81, 4, 8) (dual of [(81, 4), 316, 9]-NRT-code), using
- Reed–Solomon NRT-code RS(4;316,81) [i]
- discarding factors / shortening the dual code based on linear OOA(818, 81, F81, 4, 8) (dual of [(81, 4), 316, 9]-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(8161, 373, F81, 4, 36) (dual of [(373, 4), 1431, 37]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Digital (24, 61, 373)-net over F81 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |