Information on Result #1182572
Digital (178, 207, 1173)-net over F2, using net defined by OOA based on linear OOA(2207, 1173, F2, 29, 29) (dual of [(1173, 29), 33810, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2207, 16423, F2, 29) (dual of [16423, 16216, 30]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2204, 16420, F2, 29) (dual of [16420, 16216, 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(27, 35, F2, 3) (dual of [35, 28, 4]-code or 35-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(2204, 16420, F2, 29) (dual of [16420, 16216, 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 (179, 207, 1173)-net over F2 | [i] | t-Expansion | |
| 2 | Digital (179, 208, 1173)-net over F2 | [i] | Net Duplication | |
| 3 | Digital (180, 209, 1173)-net over F2 | [i] | ||