Information on Result #2764913
Linear OOA(2208, 2097190, F2, 4, 16) (dual of [(2097190, 4), 8388552, 17]-NRT-code), using strength reduction based on linear OOA(2208, 2097190, F2, 4, 17) (dual of [(2097190, 4), 8388552, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(221, 39, F2, 4, 8) (dual of [(39, 4), 135, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (13, 21, 39)-net over F2, using
- linear OOA(2187, 2097151, F2, 4, 17) (dual of [(2097151, 4), 8388417, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2187, 4194302, F2, 2, 17) (dual of [(4194302, 2), 8388417, 18]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2185, 4194301, F2, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2185, 8388602, F2, 17) (dual of [8388602, 8388417, 18]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 2-folding [i] based on linear OA(2185, 8388602, F2, 17) (dual of [8388602, 8388417, 18]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2185, 4194301, F2, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2187, 4194302, F2, 2, 17) (dual of [(4194302, 2), 8388417, 18]-NRT-code), using
- linear OOA(221, 39, F2, 4, 8) (dual of [(39, 4), 135, 9]-NRT-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(2208, 1878230, F2, 5, 16) (dual of [(1878230, 5), 9390942, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
2 | Linear OOA(2208, 1878230, F2, 6, 16) (dual of [(1878230, 6), 11269172, 17]-NRT-code) | [i] | ||
3 | Linear OOA(2208, 1878230, F2, 7, 16) (dual of [(1878230, 7), 13147402, 17]-NRT-code) | [i] | ||
4 | Linear OOA(2208, 1878230, F2, 8, 16) (dual of [(1878230, 8), 15025632, 17]-NRT-code) | [i] | ||
5 | Digital (192, 208, 1878230)-net over F2 | [i] |