Information on Result #1760098
Digital (213, 258, 1048)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2258, 1048, F2, 2, 45) (dual of [(1048, 2), 1838, 46]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2256, 1047, F2, 2, 45) (dual of [(1047, 2), 1838, 46]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2256, 2094, F2, 45) (dual of [2094, 1838, 46]-code), using
- construction X applied to Ce(44) ⊂ Ce(38) [i] based on
- linear OA(2243, 2048, F2, 45) (dual of [2048, 1805, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2210, 2048, F2, 39) (dual of [2048, 1838, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(213, 46, F2, 5) (dual of [46, 33, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- construction X applied to Ce(44) ⊂ Ce(38) [i] based on
- OOA 2-folding [i] based on linear OA(2256, 2094, F2, 45) (dual of [2094, 1838, 46]-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 (214, 259, 1048)-net over F2 | [i] | Net Duplication | |