Information on Result #698973
Linear OA(6473, 4128, F64, 32) (dual of [4128, 4055, 33]-code), using construction X applied to Ce(31) ⊂ Ce(20) 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(6441, 4096, F64, 21) (dual of [4096, 4055, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(6410, 32, F64, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,64)), using
- discarding factors / shortening the dual code based on linear OA(6410, 64, F64, 10) (dual of [64, 54, 11]-code or 64-arc in PG(9,64)), using
- Reed–Solomon code RS(54,64) [i]
- discarding factors / shortening the dual code based on linear OA(6410, 64, F64, 10) (dual of [64, 54, 11]-code or 64-arc in PG(9,64)), 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(3288, 4128, S32, 32) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6473, 4119, F64, 2, 32) (dual of [(4119, 2), 8165, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6473, 4119, F64, 3, 32) (dual of [(4119, 3), 12284, 33]-NRT-code) | [i] | ||
| 4 | Digital (41, 73, 4119)-net over F64 | [i] | ||
| 5 | Linear OOA(6473, 2064, F64, 2, 32) (dual of [(2064, 2), 4055, 33]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6473, 1376, F64, 3, 32) (dual of [(1376, 3), 4055, 33]-NRT-code) | [i] | ||