Information on Result #1195396
Digital (68, 86, 116511)-net over F16, using net defined by OOA based on linear OOA(1686, 116511, F16, 18, 18) (dual of [(116511, 18), 2097112, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(1686, 1048599, F16, 18) (dual of [1048599, 1048513, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(1686, 1048600, F16, 18) (dual of [1048600, 1048514, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] 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, 24, F16, 4) (dual of [24, 19, 5]-code), using
- extended algebraic-geometric code AGe(F,19P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(1686, 1048600, F16, 18) (dual of [1048600, 1048514, 19]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (69, 87, 116511)-net over F16 | [i] | Net Duplication | |