Information on Result #658690
Linear OA(1686, 106, F16, 59) (dual of [106, 20, 60]-code), using construction X applied to AG(F,4P) ⊂ AG(F,25P) based on
- linear OA(1662, 64, F16, 59) (dual of [64, 2, 60]-code), using algebraic-geometric code AG(F,4P) 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(1644, 64, F16, 38) (dual of [64, 20, 39]-code), using algebraic-geometric code AG(F,25P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(1624, 42, F16, 20) (dual of [42, 18, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(1624, 45, F16, 20) (dual of [45, 21, 21]-code), using
- extended algebraic-geometric code AGe(F,24P) [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(1624, 45, F16, 20) (dual of [45, 21, 21]-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(1686, 53, F16, 2, 59) (dual of [(53, 2), 20, 60]-NRT-code) | [i] | OOA Folding | |