Information on Result #1752425
Digital (141, 155, 838865)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2155, 838865, F2, 5, 14) (dual of [(838865, 5), 4194170, 15]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2155, 4194325, F2, 14) (dual of [4194325, 4194170, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2155, 4194327, F2, 14) (dual of [4194327, 4194172, 15]-code), using
- 1 times truncation [i] based on linear OA(2156, 4194328, F2, 15) (dual of [4194328, 4194172, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(2155, 4194304, F2, 15) (dual of [4194304, 4194149, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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(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(14) ⊂ Ce(12) [i] based on
- 1 times truncation [i] based on linear OA(2156, 4194328, F2, 15) (dual of [4194328, 4194172, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2155, 4194327, F2, 14) (dual of [4194327, 4194172, 15]-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 (142, 156, 838865)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (143, 157, 838865)-net over F2 | [i] | ||