Information on Result #698665
Linear OA(6466, 4126, F64, 29) (dual of [4126, 4060, 30]-code), using construction X applied to C([0,14]) ⊂ C([0,9]) based on
- linear OA(6457, 4097, F64, 29) (dual of [4097, 4040, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(6437, 4097, F64, 19) (dual of [4097, 4060, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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(3280, 4126, S32, 29) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6466, 3853, F64, 2, 29) (dual of [(3853, 2), 7640, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6466, 3853, F64, 3, 29) (dual of [(3853, 3), 11493, 30]-NRT-code) | [i] | ||
| 4 | Digital (37, 66, 3853)-net over F64 | [i] | ||
| 5 | Linear OOA(6466, 2063, F64, 2, 29) (dual of [(2063, 2), 4060, 30]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6466, 1375, F64, 3, 29) (dual of [(1375, 3), 4059, 30]-NRT-code) | [i] | ||