Information on Result #1315608
Linear OA(4932, 169, F49, 19) (dual of [169, 137, 20]-code), using 66 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 4 times 0, 1, 10 times 0, 1, 18 times 0, 1, 28 times 0) based on linear OA(4923, 94, F49, 19) (dual of [94, 71, 20]-code), using
- construction X applied to AG(F,71P) ⊂ AG(F,73P) [i] based on
- linear OA(4922, 91, F49, 19) (dual of [91, 69, 20]-code), using algebraic-geometric code AG(F,71P) [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
- linear OA(4920, 91, F49, 17) (dual of [91, 71, 18]-code), using algebraic-geometric code AG(F,73P) [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92 (see above)
- linear OA(491, 3, F49, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 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(4932, 169, F49, 2, 19) (dual of [(169, 2), 306, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4932, 169, F49, 3, 19) (dual of [(169, 3), 475, 20]-NRT-code) | [i] | ||
| 3 | Digital (13, 32, 169)-net over F49 | [i] | ||