Information on Result #2648592
Linear OOA(6450, large, F64, 3, 5), using strength reduction based on linear OOA(6450, large, F64, 3, 8), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(641, 65, F64, 3, 1) (dual of [(65, 3), 194, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(641, s, F64, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(641, s, F64, 3, 1) for arbitrarily large s, using
- linear OOA(642, 65, F64, 3, 2) (dual of [(65, 3), 193, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;193,64) [i]
- 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(6413, 2796201, F64, 3, 4) (dual of [(2796201, 3), 8388590, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6413, 4194301, F64, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(6413, 8388602, F64, 4) (dual of [8388602, 8388589, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(6413, large, F64, 4) (dual of [large, large−13, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(6413, large, F64, 4) (dual of [large, large−13, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(6413, 8388602, F64, 4) (dual of [8388602, 8388589, 5]-code), using
- discarding factors / shortening the dual code based on linear OOA(6413, 4194301, F64, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
- linear OOA(6429, 2796201, F64, 3, 8) (dual of [(2796201, 3), 8388574, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 3-folding [i] based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- linear OOA(641, 65, F64, 3, 1) (dual of [(65, 3), 194, 2]-NRT-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(6452, large, F64, 3, 5) | [i] | OOA Duplication | |