Information on Result #698656
Linear OA(6448, 4120, F64, 21) (dual of [4120, 4072, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,6]) based on
- 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(6425, 4097, F64, 13) (dual of [4097, 4072, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(647, 23, F64, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,64)), using
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- Reed–Solomon code RS(57,64) [i]
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), 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(3258, 4120, S32, 21) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6448, 3688, F64, 2, 21) (dual of [(3688, 2), 7328, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6448, 3688, F64, 3, 21) (dual of [(3688, 3), 11016, 22]-NRT-code) | [i] | ||
| 4 | Digital (27, 48, 3688)-net over F64 | [i] | ||
| 5 | Linear OOA(6448, 2060, F64, 2, 21) (dual of [(2060, 2), 4072, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6448, 1373, F64, 3, 21) (dual of [(1373, 3), 4071, 22]-NRT-code) | [i] | ||