Information on Result #658694
Linear OA(1680, 104, F16, 53) (dual of [104, 24, 54]-code), using construction X applied to AG(F,10P) ⊂ AG(F,29P) based on
- linear OA(1658, 64, F16, 53) (dual of [64, 6, 54]-code), using algebraic-geometric code AG(F,10P) with known gap numbers [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using the Hermitian function field over F16 [i]
- linear OA(1640, 64, F16, 34) (dual of [64, 24, 35]-code), using algebraic-geometric code AG(F,29P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(1622, 40, F16, 18) (dual of [40, 18, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(1622, 45, F16, 18) (dual of [45, 23, 19]-code), using
- extended algebraic-geometric code AGe(F,26P) [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- discarding factors / shortening the dual code based on linear OA(1622, 45, F16, 18) (dual of [45, 23, 19]-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 OA(1679, 103, F16, 52) (dual of [103, 24, 53]-code) | [i] | Truncation | |
| 2 | Linear OOA(1680, 52, F16, 2, 53) (dual of [(52, 2), 24, 54]-NRT-code) | [i] | OOA Folding | |