Information on Result #655518
Linear OA(8140, 372, F81, 23) (dual of [372, 332, 24]-code), using construction X applied to AG(F,345P) ⊂ AG(F,347P) based on
- linear OA(8139, 369, F81, 23) (dual of [369, 330, 24]-code), using algebraic-geometric code AG(F,345P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- linear OA(8137, 369, F81, 21) (dual of [369, 332, 22]-code), using algebraic-geometric code AG(F,347P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370 (see above)
- linear OA(811, 3, F81, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(8140, 371, F81, 2, 23) (dual of [(371, 2), 702, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8140, 371, F81, 3, 23) (dual of [(371, 3), 1073, 24]-NRT-code) | [i] | ||
| 3 | Linear OOA(8140, 371, F81, 4, 23) (dual of [(371, 4), 1444, 24]-NRT-code) | [i] | ||
| 4 | Digital (17, 40, 371)-net over F81 | [i] | ||
| 5 | Linear OOA(8140, 186, F81, 2, 23) (dual of [(186, 2), 332, 24]-NRT-code) | [i] | OOA Folding | |