Information on Result #1754979
Digital (166, 196, 2051)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2196, 2051, F2, 4, 30) (dual of [(2051, 4), 8008, 31]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2196, 8204, F2, 30) (dual of [8204, 8008, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2196, 8205, F2, 30) (dual of [8205, 8009, 31]-code), using
- 1 times truncation [i] based on linear OA(2197, 8206, F2, 31) (dual of [8206, 8009, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2196, 8192, F2, 31) (dual of [8192, 7996, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2183, 8192, F2, 29) (dual of [8192, 8009, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(30) ⊂ Ce(28) [i] based on
- 1 times truncation [i] based on linear OA(2197, 8206, F2, 31) (dual of [8206, 8009, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2196, 8205, F2, 30) (dual of [8205, 8009, 31]-code), using
Mode: 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 (167, 197, 2051)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (168, 198, 2051)-net over F2 | [i] | ||