Information on Result #1758712
Digital (221, 243, 599189)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2243, 599189, F2, 7, 22) (dual of [(599189, 7), 4194080, 23]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2243, 4194323, F2, 22) (dual of [4194323, 4194080, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2243, 4194327, F2, 22) (dual of [4194327, 4194084, 23]-code), using
- 1 times truncation [i] based on linear OA(2244, 4194328, F2, 23) (dual of [4194328, 4194084, 24]-code), using
- construction X4 applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2243, 4194304, F2, 23) (dual of [4194304, 4194061, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2221, 4194304, F2, 21) (dual of [4194304, 4194083, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(223, 24, F2, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
- dual of repetition code with length 24 [i]
- linear OA(21, 24, F2, 1) (dual of [24, 23, 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 X4 applied to Ce(22) ⊂ Ce(20) [i] based on
- 1 times truncation [i] based on linear OA(2244, 4194328, F2, 23) (dual of [4194328, 4194084, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2243, 4194327, F2, 22) (dual of [4194327, 4194084, 23]-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 (222, 244, 599189)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (223, 245, 599189)-net over F2 | [i] | ||