Information on Result #1009459
Linear OOA(2249, 2818046, F2, 3, 17) (dual of [(2818046, 3), 8453889, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(264, 21845, F2, 3, 8) (dual of [(21845, 3), 65471, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(264, 65535, F2, 8) (dual of [65535, 65471, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(264, 65536, F2, 8) (dual of [65536, 65472, 9]-code), using
- 1 times truncation [i] based on linear OA(265, 65537, F2, 9) (dual of [65537, 65472, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(265, 65537, F2, 9) (dual of [65537, 65472, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(264, 65536, F2, 8) (dual of [65536, 65472, 9]-code), using
- OOA 3-folding [i] based on linear OA(264, 65535, F2, 8) (dual of [65535, 65471, 9]-code), using
- linear OOA(2185, 2796201, F2, 3, 17) (dual of [(2796201, 3), 8388418, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-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(2249, 2817196, F2, 4, 17) (dual of [(2817196, 4), 11268535, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2249, 2817196, F2, 5, 17) (dual of [(2817196, 5), 14085731, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(2249, 2817196, F2, 6, 17) (dual of [(2817196, 6), 16902927, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(2249, 2817196, F2, 7, 17) (dual of [(2817196, 7), 19720123, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(2249, 2817196, F2, 8, 17) (dual of [(2817196, 8), 22537319, 18]-NRT-code) | [i] | ||
| 6 | Digital (232, 249, 2817196)-net over F2 | [i] | ||