Information on Result #1759155
Digital (210, 248, 2051)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2248, 2051, F2, 4, 38) (dual of [(2051, 4), 7956, 39]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2248, 8204, F2, 38) (dual of [8204, 7956, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(2248, 8205, F2, 38) (dual of [8205, 7957, 39]-code), using
- 1 times truncation [i] based on linear OA(2249, 8206, F2, 39) (dual of [8206, 7957, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(36) [i] based on
- linear OA(2248, 8192, F2, 39) (dual of [8192, 7944, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2235, 8192, F2, 37) (dual of [8192, 7957, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 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(38) ⊂ Ce(36) [i] based on
- 1 times truncation [i] based on linear OA(2249, 8206, F2, 39) (dual of [8206, 7957, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(2248, 8205, F2, 38) (dual of [8205, 7957, 39]-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 (211, 249, 2051)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (212, 250, 2051)-net over F2 | [i] | ||