Information on Result #1182570
Digital (174, 203, 1172)-net over F2, using net defined by OOA based on linear OOA(2203, 1172, F2, 29, 29) (dual of [(1172, 29), 33785, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2203, 16409, F2, 29) (dual of [16409, 16206, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2203, 16417, F2, 29) (dual of [16417, 16214, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- linear OA(2197, 16385, F2, 29) (dual of [16385, 16188, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2169, 16385, F2, 25) (dual of [16385, 16216, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2203, 16417, F2, 29) (dual of [16417, 16214, 30]-code), using
Mode: Constructive and 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 (175, 203, 1172)-net over F2 | [i] | t-Expansion | |
| 2 | Digital (175, 204, 1172)-net over F2 | [i] | Net Duplication | |
| 3 | Digital (176, 205, 1172)-net over F2 | [i] | ||
| 4 | Digital (177, 206, 1172)-net over F2 | [i] | ||