Information on Result #1203550
Digital (27, 41, 299594)-net over F128, using net defined by OOA based on linear OOA(12841, 299594, F128, 14, 14) (dual of [(299594, 14), 4194275, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(12841, 2097158, F128, 14) (dual of [2097158, 2097117, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(12841, 2097159, F128, 14) (dual of [2097159, 2097118, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(12841, 2097159, F128, 14) (dual of [2097159, 2097118, 15]-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 (28, 42, 299594)-net over F128 | [i] | Net Duplication | |
| 2 | Digital (35, 49, 299744)-net over F128 | [i] | (u, u+v)-Construction for Nets | |