Information on Result #1079742
Linear OOA(2173, 2099197, F2, 4, 13) (dual of [(2099197, 4), 8396615, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(234, 2047, F2, 4, 6) (dual of [(2047, 4), 8154, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (28, 34, 2047)-net over F2, using
- 1 times m-reduction [i] based on digital (28, 35, 2047)-net over F2, using
- extracting embedded OOA [i] based on digital (28, 34, 2047)-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(2173, 2099197, F2, 4, 12) (dual of [(2099197, 4), 8396615, 13]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2174, 2099197, F2, 4, 13) (dual of [(2099197, 4), 8396614, 14]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2237, 4196346, F2, 4, 13) (dual of [(4196346, 4), 16785147, 14]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 4 | Linear OOA(2238, 4196347, F2, 4, 13) (dual of [(4196347, 4), 16785150, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(2240, 4198394, F2, 4, 13) (dual of [(4198394, 4), 16793336, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(2237, 4196347, F2, 4, 13) (dual of [(4196347, 4), 16785151, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(2173, 2099197, F2, 5, 13) (dual of [(2099197, 5), 10495812, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 8 | Linear OOA(2173, 2099197, F2, 6, 13) (dual of [(2099197, 6), 12595009, 14]-NRT-code) | [i] | ||
| 9 | Linear OOA(2173, 2099197, F2, 7, 13) (dual of [(2099197, 7), 14694206, 14]-NRT-code) | [i] | ||
| 10 | Linear OOA(2173, 2099197, F2, 8, 13) (dual of [(2099197, 8), 16793403, 14]-NRT-code) | [i] | ||
| 11 | Digital (160, 173, 2099197)-net over F2 | [i] | ||