Information on Result #1756552
Digital (197, 217, 349533)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2217, 349533, F2, 6, 20) (dual of [(349533, 6), 2096981, 21]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2217, 2097198, F2, 20) (dual of [2097198, 2096981, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2217, 2097201, F2, 20) (dual of [2097201, 2096984, 21]-code), using
- 1 times truncation [i] based on linear OA(2218, 2097202, F2, 21) (dual of [2097202, 2096984, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2211, 2097153, F2, 21) (dual of [2097153, 2096942, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2169, 2097153, F2, 17) (dual of [2097153, 2096984, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(27, 49, F2, 3) (dual of [49, 42, 4]-code or 49-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([0,10]) ⊂ C([0,8]) [i] based on
- 1 times truncation [i] based on linear OA(2218, 2097202, F2, 21) (dual of [2097202, 2096984, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2217, 2097201, F2, 20) (dual of [2097201, 2096984, 21]-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 (198, 218, 349533)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (199, 219, 349533)-net over F2 | [i] | ||