Information on Result #1754282
Digital (159, 186, 3280)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2186, 3280, F2, 5, 27) (dual of [(3280, 5), 16214, 28]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2185, 3280, F2, 5, 27) (dual of [(3280, 5), 16215, 28]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2185, 16400, F2, 27) (dual of [16400, 16215, 28]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2184, 16399, F2, 27) (dual of [16399, 16215, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2169, 16384, F2, 25) (dual of [16384, 16215, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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(26) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2184, 16399, F2, 27) (dual of [16399, 16215, 28]-code), using
- OOA 5-folding [i] based on linear OA(2185, 16400, F2, 27) (dual of [16400, 16215, 28]-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 (160, 187, 3280)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (161, 188, 3280)-net over F2 | [i] | ||