Information on Result #1022458
Linear OOA(6437, large, F64, 3, 7), using generalized (u, u+v)-construction based on
- linear OOA(645, 2796201, F64, 3, 2) (dual of [(2796201, 3), 8388598, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(645, large, F64, 3, 2), using
- appending 1 arbitrary column [i] based on linear OOA(645, large, F64, 2, 2), using
- appending kth column [i] based on linear OA(645, large, F64, 2) (dual of [large, large−5, 3]-code), using
- Hamming code H(5,64) [i]
- appending kth column [i] based on linear OA(645, large, F64, 2) (dual of [large, large−5, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(645, large, F64, 2, 2), using
- discarding factors / shortening the dual code based on linear OOA(645, large, F64, 3, 2), using
- linear OOA(647, 2796201, F64, 3, 3) (dual of [(2796201, 3), 8388596, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(647, 8388602, F64, 3, 3) (dual of [(8388602, 3), 25165799, 4]-NRT-code), using
- OOA stacking with additional row [i] based on linear OA(647, large, F64, 3) (dual of [large, large−7, 4]-code), using
- discarding factors / shortening the dual code based on linear OOA(647, 8388602, F64, 3, 3) (dual of [(8388602, 3), 25165799, 4]-NRT-code), using
- linear OOA(6425, 2796201, F64, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, 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(6437, large, F64, 3, 6) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(6437, large, F64, 3, 5) | [i] | ||
| 3 | Linear OOA(6437, large, F64, 3, 4) | [i] | ||
| 4 | Linear OOA(6437, large, F64, 3, 3) | [i] | ||
| 5 | Linear OOA(6440, large, F64, 3, 7) | [i] | NRT-Code Embedding in Larger Space | |
| 6 | Linear OOA(6443, large, F64, 3, 7) | [i] | ||
| 7 | Linear OOA(6446, large, F64, 3, 7) | [i] | ||
| 8 | Linear OOA(6452, large, F64, 3, 7) | [i] | ||
| 9 | Linear OOA(6464, large, F64, 3, 7) | [i] | ||
| 10 | Linear OOA(6476, large, F64, 3, 7) | [i] | ||
| 11 | Linear OOA(6485, large, F64, 3, 7) | [i] | ||
| 12 | Linear OOA(6437, 8388602, F64, 9, 7) (dual of [(8388602, 9), 75497381, 8]-NRT-code) | [i] | OOA Stacking with Additional Row | |