Information on Result #1665060
Linear OOA(2154, 2097192, F2, 6, 12) (dual of [(2097192, 6), 12582998, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2154, 2097192, F2, 4, 12) (dual of [(2097192, 4), 8388614, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(216, 42, F2, 4, 6) (dual of [(42, 4), 152, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (10, 16, 42)-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
- linear OOA(216, 42, F2, 4, 6) (dual of [(42, 4), 152, 7]-NRT-code), using
Mode: 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(2154, 2097191, F2, 7, 12) (dual of [(2097191, 7), 14680183, 13]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(2154, 2097191, F2, 8, 12) (dual of [(2097191, 8), 16777374, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(2154, 2097191, F2, 18, 12) (dual of [(2097191, 18), 37749284, 13]-NRT-code) | [i] | ||