Information on Result #1080082
Linear OOA(2219, 2097229, F2, 4, 17) (dual of [(2097229, 4), 8388697, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(232, 78, F2, 4, 8) (dual of [(78, 4), 280, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(211, 47, F2, 4, 4) (dual of [(47, 4), 177, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(211, 47, F2, 3, 4) (dual of [(47, 3), 130, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 11, 47)-net over F2, using
- appending kth column [i] based on linear OOA(211, 47, F2, 3, 4) (dual of [(47, 3), 130, 5]-NRT-code), using
- 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(211, 47, F2, 4, 4) (dual of [(47, 4), 177, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- 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
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(2219, 2097229, F2, 4, 16) (dual of [(2097229, 4), 8388697, 17]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2220, 2097229, F2, 4, 17) (dual of [(2097229, 4), 8388696, 18]-NRT-code) | [i] | OOA Duplication | |