Information on Result #1751379
Digital (111, 134, 1027)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2134, 1027, F2, 4, 23) (dual of [(1027, 4), 3974, 24]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2134, 4108, F2, 23) (dual of [4108, 3974, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2134, 4109, F2, 23) (dual of [4109, 3975, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2133, 4096, F2, 23) (dual of [4096, 3963, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2121, 4096, F2, 21) (dual of [4096, 3975, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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(22) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2134, 4109, F2, 23) (dual of [4109, 3975, 24]-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 (112, 135, 1027)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (113, 136, 1027)-net over F2 | [i] | ||