Information on Result #1179082
Digital (7, 11, 1048580)-net over F128, using net defined by OOA based on linear OOA(12811, 1048580, F128, 4, 4) (dual of [(1048580, 4), 4194309, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(12811, 2097160, F128, 4) (dual of [2097160, 2097149, 5]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1284, 2097152, F128, 2) (dual of [2097152, 2097148, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(1287, 8, F128, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,128)), using
- dual of repetition code with length 8 [i]
- linear OA(1281, 8, F128, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, 128, F128, 1) (dual of [128, 127, 2]-code), using
- Reed–Solomon code RS(127,128) [i]
- discarding factors / shortening the dual code based on linear OA(1281, 128, F128, 1) (dual of [128, 127, 2]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
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 (32, 40, 3145730)-net over F128 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (35, 44, 3145730)-net over F128 | [i] | ||
| 3 | Digital (65, 77, 3844780)-net over F128 | [i] | Generalized (u, u+v)-Construction for Nets | |