Information on Result #698639
Linear OA(6450, 4114, F64, 23) (dual of [4114, 4064, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,8]) based on
- linear OA(6445, 4097, F64, 23) (dual of [4097, 4052, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(6433, 4097, F64, 17) (dual of [4097, 4064, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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 | Linear OA(8100, 8228, F8, 23) (dual of [8228, 8128, 24]-code) | [i] | Trace Code | |
| 2 | OA(3260, 4114, S32, 23) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(6450, 2248, F64, 2, 23) (dual of [(2248, 2), 4446, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(6450, 2248, F64, 3, 23) (dual of [(2248, 3), 6694, 24]-NRT-code) | [i] | ||
| 5 | Digital (27, 50, 2248)-net over F64 | [i] | ||
| 6 | Linear OOA(6450, 2057, F64, 2, 23) (dual of [(2057, 2), 4064, 24]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(6450, 1371, F64, 3, 23) (dual of [(1371, 3), 4063, 24]-NRT-code) | [i] | ||