Information on Result #1753893
Digital (158, 180, 13111)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2180, 13111, F2, 5, 22) (dual of [(13111, 5), 65375, 23]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2180, 65555, F2, 22) (dual of [65555, 65375, 23]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2177, 65552, F2, 22) (dual of [65552, 65375, 23]-code), using
- 1 times truncation [i] based on linear OA(2178, 65553, F2, 23) (dual of [65553, 65375, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2177, 65536, F2, 23) (dual of [65536, 65359, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2161, 65536, F2, 21) (dual of [65536, 65375, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 17, F2, 1) (dual of [17, 16, 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
- 1 times truncation [i] based on linear OA(2178, 65553, F2, 23) (dual of [65553, 65375, 24]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2177, 65552, F2, 22) (dual of [65552, 65375, 23]-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 (159, 181, 13111)-net over F2 | [i] | Net Duplication | |