Information on Result #989410
Linear OOA(6437, 1366, F64, 3, 19) (dual of [(1366, 3), 4061, 20]-NRT-code), using OOA 3-folding based on linear OA(6437, 4098, F64, 19) (dual of [4098, 4061, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(6437, 4096, F64, 19) (dual of [4096, 4059, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(6435, 4096, F64, 18) (dual of [4096, 4061, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(6446, 1431, F64, 3, 19) (dual of [(1431, 3), 4247, 20]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(6447, 1446, F64, 3, 19) (dual of [(1446, 3), 4291, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(6449, 1470, F64, 3, 19) (dual of [(1470, 3), 4361, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(6450, 1496, F64, 3, 19) (dual of [(1496, 3), 4438, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(6451, 1511, F64, 3, 19) (dual of [(1511, 3), 4482, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(6452, 1526, F64, 3, 19) (dual of [(1526, 3), 4526, 20]-NRT-code) | [i] | ||
| 7 | Linear OOA(6453, 1543, F64, 3, 19) (dual of [(1543, 3), 4576, 20]-NRT-code) | [i] | ||
| 8 | Linear OOA(6453, 1561, F64, 3, 19) (dual of [(1561, 3), 4630, 20]-NRT-code) | [i] | ||
| 9 | Digital (18, 37, 1259)-net over F64 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |