Information on Result #698957
Linear OA(6472, 4125, F64, 32) (dual of [4125, 4053, 33]-code), using construction X applied to Ce(31) ⊂ Ce(21) based on
- linear OA(6463, 4096, F64, 32) (dual of [4096, 4033, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(6443, 4096, F64, 22) (dual of [4096, 4053, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(649, 29, F64, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,64)), using
- discarding factors / shortening the dual code based on linear OA(649, 64, F64, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), using
- Reed–Solomon code RS(55,64) [i]
- discarding factors / shortening the dual code based on linear OA(649, 64, F64, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), 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 | OA(3287, 4125, S32, 32) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6472, 3584, F64, 2, 32) (dual of [(3584, 2), 7096, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6472, 3584, F64, 3, 32) (dual of [(3584, 3), 10680, 33]-NRT-code) | [i] | ||
| 4 | Digital (40, 72, 3584)-net over F64 | [i] | ||
| 5 | Linear OOA(6472, 2062, F64, 2, 32) (dual of [(2062, 2), 4052, 33]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6472, 1375, F64, 3, 32) (dual of [(1375, 3), 4053, 33]-NRT-code) | [i] | ||