Information on Result #1116003
Linear OOA(2228, 1677749, F2, 5, 18) (dual of [(1677749, 5), 8388517, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(221, 29, F2, 5, 9) (dual of [(29, 5), 124, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 21, 29)-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(2230, 1677749, F2, 5, 18) (dual of [(1677749, 5), 8388515, 19]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2231, 1677749, F2, 5, 18) (dual of [(1677749, 5), 8388514, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2228, 1677749, F2, 6, 18) (dual of [(1677749, 6), 10066266, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2228, 1677749, F2, 7, 18) (dual of [(1677749, 7), 11744015, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(2228, 1677749, F2, 8, 18) (dual of [(1677749, 8), 13421764, 19]-NRT-code) | [i] | ||
| 6 | Digital (210, 228, 1677749)-net over F2 | [i] | ||