Information on Result #1051310
Linear OOA(292, 65541, F2, 4, 11) (dual of [(65541, 4), 262072, 12]-NRT-code), using OOA 4-folding based on linear OA(292, 262164, F2, 11) (dual of [262164, 262072, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(291, 262144, F2, 11) (dual of [262144, 262053, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(273, 262144, F2, 9) (dual of [262144, 262071, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(219, 20, F2, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
- dual of repetition code with length 20 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 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
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(293, 65541, F2, 4, 11) (dual of [(65541, 4), 262071, 12]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(294, 65541, F2, 4, 11) (dual of [(65541, 4), 262070, 12]-NRT-code) | [i] | ||
| 3 | Linear OOA(295, 65541, F2, 4, 11) (dual of [(65541, 4), 262069, 12]-NRT-code) | [i] | ||
| 4 | Linear OOA(292, 65541, F2, 5, 11) (dual of [(65541, 5), 327613, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(292, 65541, F2, 6, 11) (dual of [(65541, 6), 393154, 12]-NRT-code) | [i] | ||
| 6 | Linear OOA(292, 65541, F2, 7, 11) (dual of [(65541, 7), 458695, 12]-NRT-code) | [i] | ||
| 7 | Linear OOA(292, 65541, F2, 8, 11) (dual of [(65541, 8), 524236, 12]-NRT-code) | [i] | ||
| 8 | Digital (81, 92, 65541)-net over F2 | [i] | ||