Information on Result #935658
Linear OOA(4955, 346, F49, 2, 31) (dual of [(346, 2), 637, 32]-NRT-code), using construction X applied to AG(2;F,654P) ⊂ AG(2;F,658P) based on
- linear OOA(4952, 343, F49, 2, 31) (dual of [(343, 2), 634, 32]-NRT-code), using algebraic-geometric NRT-code AG(2;F,654P) [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- linear OOA(4948, 343, F49, 2, 27) (dual of [(343, 2), 638, 28]-NRT-code), using algebraic-geometric NRT-code AG(2;F,658P) [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344 (see above)
- linear OOA(493, 3, F49, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(493, 49, F49, 2, 3) (dual of [(49, 2), 95, 4]-NRT-code), using
- Reed–Solomon NRT-code RS(2;95,49) [i]
- discarding factors / shortening the dual code based on linear OOA(493, 49, F49, 2, 3) (dual of [(49, 2), 95, 4]-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(4955, 346, F49, 3, 31) (dual of [(346, 3), 983, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (24, 55, 346)-net over F49 | [i] | ||