Information on Result #1751388
Digital (122, 134, 1048582)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2134, 1048582, F2, 4, 12) (dual of [(1048582, 4), 4194194, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2134, 4194328, F2, 12) (dual of [4194328, 4194194, 13]-code), using
- strength reduction [i] based on linear OA(2134, 4194328, F2, 13) (dual of [4194328, 4194194, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(2133, 4194304, F2, 13) (dual of [4194304, 4194171, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2111, 4194304, F2, 11) (dual of [4194304, 4194193, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(223, 24, F2, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
- dual of repetition code with length 24 [i]
- linear OA(21, 24, F2, 1) (dual of [24, 23, 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 X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- strength reduction [i] based on linear OA(2134, 4194328, F2, 13) (dual of [4194328, 4194194, 14]-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 (123, 135, 1048582)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (124, 136, 1048582)-net over F2 | [i] | ||
| 3 | Digital (125, 137, 1048582)-net over F2 | [i] | ||