Information on Result #1079732
Linear OOA(2158, 2097222, F2, 4, 13) (dual of [(2097222, 4), 8388730, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(219, 72, F2, 4, 6) (dual of [(72, 4), 269, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (13, 19, 72)-net over F2, using
- linear OOA(2139, 2097150, F2, 4, 13) (dual of [(2097150, 4), 8388461, 14]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2139, 8388600, F2, 13) (dual of [8388600, 8388461, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- OOA 4-folding [i] based on linear OA(2139, 8388600, F2, 13) (dual of [8388600, 8388461, 14]-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(2225, 4194444, F2, 4, 13) (dual of [(4194444, 4), 16777551, 14]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2158, 2097222, F2, 5, 13) (dual of [(2097222, 5), 10485952, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2158, 2097222, F2, 6, 13) (dual of [(2097222, 6), 12583174, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(2158, 2097222, F2, 7, 13) (dual of [(2097222, 7), 14680396, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(2158, 2097222, F2, 8, 13) (dual of [(2097222, 8), 16777618, 14]-NRT-code) | [i] | ||
| 6 | Digital (145, 158, 2097222)-net over F2 | [i] | ||