Information on Result #698664
Linear OA(6470, 4126, F64, 31) (dual of [4126, 4056, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,10]) based on
- linear OA(6461, 4097, F64, 31) (dual of [4097, 4036, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(6441, 4097, F64, 21) (dual of [4097, 4056, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [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(3284, 4126, S32, 31) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6470, 3661, F64, 2, 31) (dual of [(3661, 2), 7252, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6470, 3661, F64, 3, 31) (dual of [(3661, 3), 10913, 32]-NRT-code) | [i] | ||
| 4 | Digital (39, 70, 3661)-net over F64 | [i] | ||
| 5 | Linear OOA(6470, 2063, F64, 2, 31) (dual of [(2063, 2), 4056, 32]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6470, 1375, F64, 3, 31) (dual of [(1375, 3), 4055, 32]-NRT-code) | [i] | ||