Information on Result #2478282
Linear OOA(2209, large, F2, 2, 13), using 21 times duplication based on linear OOA(2208, large, F2, 2, 13), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2206, 8388602, F2, 2, 13) (dual of [(8388602, 2), 16776998, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(267, 4194303, F2, 2, 6) (dual of [(4194303, 2), 8388539, 7]-NRT-code), using
- linear OOA(2139, 4194301, F2, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 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 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 14]-code), using
- (u, u+v)-construction [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, 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(2209, 7714298, F2, 3, 13) (dual of [(7714298, 3), 23142685, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2209, 7714298, F2, 4, 13) (dual of [(7714298, 4), 30856983, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(2209, 7714298, F2, 5, 13) (dual of [(7714298, 5), 38571281, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(2209, 7714298, F2, 6, 13) (dual of [(7714298, 6), 46285579, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(2209, 7714298, F2, 7, 13) (dual of [(7714298, 7), 53999877, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(2209, 7714298, F2, 8, 13) (dual of [(7714298, 8), 61714175, 14]-NRT-code) | [i] | ||
| 7 | Digital (196, 209, 7714298)-net over F2 | [i] | ||