Information on Result #1750111
Digital (82, 100, 686)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2100, 686, F2, 3, 18) (dual of [(686, 3), 1958, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2100, 2058, F2, 18) (dual of [2058, 1958, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2100, 2059, F2, 18) (dual of [2059, 1959, 19]-code), using
- 1 times truncation [i] based on linear OA(2101, 2060, F2, 19) (dual of [2060, 1959, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(2100, 2048, F2, 19) (dual of [2048, 1948, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(289, 2048, F2, 17) (dual of [2048, 1959, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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(18) ⊂ Ce(16) [i] based on
- 1 times truncation [i] based on linear OA(2101, 2060, F2, 19) (dual of [2060, 1959, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2100, 2059, F2, 18) (dual of [2059, 1959, 19]-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 (83, 101, 686)-net over F2 | [i] | Net Duplication | |