Information on Result #1022162
Linear OOA(6420, large, F64, 3, 5), using generalized (u, u+v)-construction based on
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(640, s, F64, 3, 0) for arbitrarily large s, using
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(640, 131073, F64, 3, 0) (dual of [(131073, 3), 393219, 1]-NRT-code) (see above)
- linear OOA(641, 131073, F64, 3, 1) (dual of [(131073, 3), 393218, 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(641, 131073, F64, 3, 1) (dual of [(131073, 3), 393218, 2]-NRT-code) (see above)
- linear OOA(641, 131073, F64, 3, 1) (dual of [(131073, 3), 393218, 2]-NRT-code) (see above)
- linear OOA(644, 131073, F64, 3, 2) (dual of [(131073, 3), 393215, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(644, 266305, F64, 3, 2) (dual of [(266305, 3), 798911, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(644, 266305, F64, 2, 2) (dual of [(266305, 2), 532606, 3]-NRT-code), using
- appending kth column [i] based on linear OA(644, 266305, F64, 2) (dual of [266305, 266301, 3]-code), using
- Hamming code H(4,64) [i]
- appending kth column [i] based on linear OA(644, 266305, F64, 2) (dual of [266305, 266301, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(644, 266305, F64, 2, 2) (dual of [(266305, 2), 532606, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(644, 266305, F64, 3, 2) (dual of [(266305, 3), 798911, 3]-NRT-code), using
- linear OOA(6413, 131073, F64, 3, 5) (dual of [(131073, 3), 393206, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(6413, 262147, F64, 5) (dual of [262147, 262134, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(6413, 262144, F64, 5) (dual of [262144, 262131, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(6413, 262147, F64, 5) (dual of [262147, 262134, 6]-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(6420, large, F64, 3, 4) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(6420, large, F64, 3, 3) | [i] | ||
| 3 | Linear OOA(6423, large, F64, 3, 5) | [i] | NRT-Code Embedding in Larger Space | |
| 4 | Linear OOA(6426, large, F64, 3, 5) | [i] | ||
| 5 | Linear OOA(6429, large, F64, 3, 5) | [i] | ||
| 6 | Linear OOA(6432, large, F64, 3, 5) | [i] | ||
| 7 | Linear OOA(6441, large, F64, 3, 5) | [i] | ||
| 8 | Linear OOA(6444, large, F64, 3, 5) | [i] | ||
| 9 | Linear OOA(6462, large, F64, 3, 5) | [i] | ||
| 10 | Linear OOA(6477, large, F64, 3, 5) | [i] | ||
| 11 | Linear OOA(6480, large, F64, 3, 5) | [i] | ||
| 12 | Linear OOA(6489, large, F64, 3, 5) | [i] | ||
| 13 | Linear OOA(6421, large, F64, 3, 5) | [i] | OOA Duplication | |