Information on Result #1179164
Digital (45, 54, 2051)-net over F2, using net defined by OOA based on linear OOA(254, 2051, F2, 9, 9) (dual of [(2051, 9), 18405, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(254, 2051, F2, 8, 9) (dual of [(2051, 8), 16354, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(254, 8205, F2, 9) (dual of [8205, 8151, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(254, 8206, F2, 9) (dual of [8206, 8152, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(253, 8192, F2, 9) (dual of [8192, 8139, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(240, 8192, F2, 7) (dual of [8192, 8152, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(254, 8206, F2, 9) (dual of [8206, 8152, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(254, 8205, F2, 9) (dual of [8205, 8151, 10]-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 (46, 54, 2051)-net over F2 | [i] | t-Expansion | |
| 2 | Digital (46, 55, 2051)-net over F2 | [i] | Net Duplication | |