Information on Result #1115999
Linear OOA(2224, 1677737, F2, 5, 18) (dual of [(1677737, 5), 8388461, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(217, 17, F2, 5, 9) (dual of [(17, 5), 68, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 17, 17)-net over F2, using
- linear OOA(2207, 1677720, F2, 5, 18) (dual of [(1677720, 5), 8388393, 19]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- OOA 5-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-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(2224, 1648748, F2, 6, 18) (dual of [(1648748, 6), 9892264, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2224, 1648748, F2, 7, 18) (dual of [(1648748, 7), 11541012, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2224, 1648748, F2, 8, 18) (dual of [(1648748, 8), 13189760, 19]-NRT-code) | [i] | ||
| 4 | Digital (206, 224, 1648748)-net over F2 | [i] | ||