Information on Result #1316263
Linear OA(12873, 620, F128, 43) (dual of [620, 547, 44]-code), using 40 step Varšamov–Edel lengthening with (ri) = (1, 39 times 0) based on linear OA(12872, 579, F128, 43) (dual of [579, 507, 44]-code), using
- construction X applied to AG(F,532P) ⊂ AG(F,534P) [i] based on
- linear OA(12871, 576, F128, 43) (dual of [576, 505, 44]-code), using algebraic-geometric code AG(F,532P) [i] based on function field F/F128 with g(F) = 28 and N(F) ≥ 577, using
- linear OA(12869, 576, F128, 41) (dual of [576, 507, 42]-code), using algebraic-geometric code AG(F,534P) [i] based on function field F/F128 with g(F) = 28 and N(F) ≥ 577 (see above)
- linear OA(1281, 3, F128, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: 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(12873, 620, F128, 2, 43) (dual of [(620, 2), 1167, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12873, 620, F128, 3, 43) (dual of [(620, 3), 1787, 44]-NRT-code) | [i] | ||
| 3 | Linear OOA(12873, 620, F128, 4, 43) (dual of [(620, 4), 2407, 44]-NRT-code) | [i] | ||
| 4 | Digital (30, 73, 620)-net over F128 | [i] | ||