Information on Result #1115882
Linear OOA(2197, 1677731, F2, 5, 16) (dual of [(1677731, 5), 8388458, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(213, 11, F2, 5, 8) (dual of [(11, 5), 42, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 13, 11)-net over F2, using
- linear OOA(2184, 1677720, F2, 5, 16) (dual of [(1677720, 5), 8388416, 17]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- OOA 5-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-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(2197, 1677731, F2, 6, 16) (dual of [(1677731, 6), 10066189, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2197, 1677731, F2, 7, 16) (dual of [(1677731, 7), 11743920, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(2197, 1677731, F2, 8, 16) (dual of [(1677731, 8), 13421651, 17]-NRT-code) | [i] | ||
| 4 | Digital (181, 197, 1677731)-net over F2 | [i] | ||