Information on Result #989936
Linear OOA(6457, 1366, F64, 3, 29) (dual of [(1366, 3), 4041, 30]-NRT-code), using OOA 3-folding based on linear OA(6457, 4098, F64, 29) (dual of [4098, 4041, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(6457, 4096, F64, 29) (dual of [4096, 4039, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(6455, 4096, F64, 28) (dual of [4096, 4041, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 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
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(6471, 1431, F64, 3, 29) (dual of [(1431, 3), 4222, 30]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(6472, 1446, F64, 3, 29) (dual of [(1446, 3), 4266, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(6474, 1470, F64, 3, 29) (dual of [(1470, 3), 4336, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(6476, 1494, F64, 3, 29) (dual of [(1494, 3), 4406, 30]-NRT-code) | [i] | ||
| 5 | Linear OOA(6478, 1543, F64, 3, 29) (dual of [(1543, 3), 4551, 30]-NRT-code) | [i] | ||
| 6 | Linear OOA(6482, 1550, F64, 3, 29) (dual of [(1550, 3), 4568, 30]-NRT-code) | [i] | ||
| 7 | Linear OOA(6482, 1561, F64, 3, 29) (dual of [(1561, 3), 4601, 30]-NRT-code) | [i] | ||
| 8 | Digital (28, 57, 1275)-net over F64 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |