Information on Result #1079517
Linear OOA(2128, 2097186, F2, 4, 11) (dual of [(2097186, 4), 8388616, 12]-NRT-code), using (u, u+v)-construction based on
- linear OOA(212, 36, F2, 4, 5) (dual of [(36, 4), 132, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 12, 36)-net over F2, using
- linear OOA(2116, 2097150, F2, 4, 11) (dual of [(2097150, 4), 8388484, 12]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2116, 8388600, F2, 11) (dual of [8388600, 8388484, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2116, large, F2, 11) (dual of [large, large−116, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(2116, large, F2, 11) (dual of [large, large−116, 12]-code), using
- OOA 4-folding [i] based on linear OA(2116, 8388600, F2, 11) (dual of [8388600, 8388484, 12]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(2174, 4194372, F2, 4, 11) (dual of [(4194372, 4), 16777314, 12]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2128, 2097186, F2, 5, 11) (dual of [(2097186, 5), 10485802, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2128, 2097186, F2, 6, 11) (dual of [(2097186, 6), 12582988, 12]-NRT-code) | [i] | ||
| 4 | Linear OOA(2128, 2097186, F2, 7, 11) (dual of [(2097186, 7), 14680174, 12]-NRT-code) | [i] | ||
| 5 | Linear OOA(2128, 2097186, F2, 8, 11) (dual of [(2097186, 8), 16777360, 12]-NRT-code) | [i] | ||
| 6 | Digital (117, 128, 2097186)-net over F2 | [i] | ||