Information on Result #1080127
Linear OOA(2231, 2097180, F2, 4, 19) (dual of [(2097180, 4), 8388489, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(221, 29, F2, 4, 9) (dual of [(29, 4), 95, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 21, 29)-net over F2, using
- linear OOA(2210, 2097151, F2, 4, 19) (dual of [(2097151, 4), 8388394, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2210, 4194302, F2, 2, 19) (dual of [(4194302, 2), 8388394, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2208, 4194301, F2, 2, 19) (dual of [(4194301, 2), 8388394, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2208, 8388602, F2, 19) (dual of [8388602, 8388394, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 2-folding [i] based on linear OA(2208, 8388602, F2, 19) (dual of [8388602, 8388394, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2208, 4194301, F2, 2, 19) (dual of [(4194301, 2), 8388394, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2210, 4194302, F2, 2, 19) (dual of [(4194302, 2), 8388394, 20]-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(2231, 2097180, F2, 4, 18) (dual of [(2097180, 4), 8388489, 19]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2232, 2097180, F2, 4, 19) (dual of [(2097180, 4), 8388488, 20]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2231, 1048590, F2, 8, 19) (dual of [(1048590, 8), 8388489, 20]-NRT-code) | [i] | OOA Folding | |