Information on Result #1303912
Linear OA(1686, 1048601, F16, 18) (dual of [1048601, 1048515, 19]-code), using construction X applied to Ce(17) ⊂ Ce(12) based on
- linear OA(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1661, 1048576, F16, 13) (dual of [1048576, 1048515, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(165, 25, F16, 4) (dual of [25, 20, 5]-code), using
- extended algebraic-geometric code AGe(F,20P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 25, 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(1686, 1048601, F16, 2, 18) (dual of [(1048601, 2), 2097116, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (68, 86, 1048601)-net over F16 | [i] | ||
| 3 | Linear OA(1687, 1048603, F16, 18) (dual of [1048603, 1048516, 19]-code) | [i] | Construction X with Varšamov Bound | |