Information on Result #1195510
Digital (77, 98, 104859)-net over F16, using net defined by OOA based on linear OOA(1698, 104859, F16, 21, 21) (dual of [(104859, 21), 2201941, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(1698, 1048591, F16, 21) (dual of [1048591, 1048493, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(1698, 1048593, F16, 21) (dual of [1048593, 1048495, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 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(162, 17, F16, 2) (dual of [17, 15, 3]-code or 17-arc in PG(1,16)), using
- extended Reed–Solomon code RSe(15,16) [i]
- Hamming code H(2,16) [i]
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(1698, 1048593, F16, 21) (dual of [1048593, 1048495, 22]-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 (78, 99, 104859)-net over F16 | [i] | Net Duplication | |
| 2 | Digital (79, 100, 104859)-net over F16 | [i] | ||
| 3 | Digital (93, 114, 104924)-net over F16 | [i] | (u, u+v)-Construction for Nets | |