Information on Result #1079604
Linear OOA(2153, 2097186, F2, 4, 12) (dual of [(2097186, 4), 8388591, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(215, 36, F2, 4, 6) (dual of [(36, 4), 129, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (9, 15, 36)-net over F2, using
- linear OOA(2138, 2097150, F2, 4, 12) (dual of [(2097150, 4), 8388462, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2138, 8388600, F2, 12) (dual of [8388600, 8388462, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- OOA 4-folding [i] based on linear OA(2138, 8388600, F2, 12) (dual of [8388600, 8388462, 13]-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(2220, 4194372, F2, 4, 12) (dual of [(4194372, 4), 16777268, 13]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2153, 2097186, F2, 5, 12) (dual of [(2097186, 5), 10485777, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2153, 2097186, F2, 6, 12) (dual of [(2097186, 6), 12582963, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(2153, 2097186, F2, 7, 12) (dual of [(2097186, 7), 14680149, 13]-NRT-code) | [i] | ||
| 5 | Linear OOA(2153, 2097186, F2, 8, 12) (dual of [(2097186, 8), 16777335, 13]-NRT-code) | [i] | ||
| 6 | Digital (141, 153, 2097186)-net over F2 | [i] | ||