Information on Result #698641
Linear OA(6442, 4114, F64, 19) (dual of [4114, 4072, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,6]) based on
- 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(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(645, 17, F64, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), 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(3251, 4114, S32, 19) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6442, 2579, F64, 2, 19) (dual of [(2579, 2), 5116, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6442, 2579, F64, 3, 19) (dual of [(2579, 3), 7695, 20]-NRT-code) | [i] | ||
| 4 | Digital (23, 42, 2579)-net over F64 | [i] | ||
| 5 | Linear OOA(6442, 2057, F64, 2, 19) (dual of [(2057, 2), 4072, 20]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6442, 1371, F64, 3, 19) (dual of [(1371, 3), 4071, 20]-NRT-code) | [i] | ||
| 7 | Linear OOA(6442, 457, F64, 19, 19) (dual of [(457, 19), 8641, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |