Information on Result #698659
Linear OA(6490, 4126, F64, 41) (dual of [4126, 4036, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,15]) based on
- linear OA(6481, 4097, F64, 41) (dual of [4097, 4016, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- 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(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(32108, 4126, S32, 41) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6490, 3216, F64, 2, 41) (dual of [(3216, 2), 6342, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6490, 3216, F64, 3, 41) (dual of [(3216, 3), 9558, 42]-NRT-code) | [i] | ||
| 4 | Digital (49, 90, 3216)-net over F64 | [i] | ||
| 5 | Linear OOA(6490, 2063, F64, 2, 41) (dual of [(2063, 2), 4036, 42]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6490, 1375, F64, 3, 41) (dual of [(1375, 3), 4035, 42]-NRT-code) | [i] | ||