Information on Result #698642
Linear OA(6438, 4114, F64, 17) (dual of [4114, 4076, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,5]) based on
- 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(6421, 4097, F64, 11) (dual of [4097, 4076, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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(3246, 4114, S32, 17) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6438, 2902, F64, 2, 17) (dual of [(2902, 2), 5766, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6438, 2902, F64, 3, 17) (dual of [(2902, 3), 8668, 18]-NRT-code) | [i] | ||
| 4 | Digital (21, 38, 2902)-net over F64 | [i] | ||
| 5 | Linear OOA(6438, 2057, F64, 2, 17) (dual of [(2057, 2), 4076, 18]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6438, 1371, F64, 3, 17) (dual of [(1371, 3), 4075, 18]-NRT-code) | [i] | ||
| 7 | Linear OOA(6438, 514, F64, 17, 17) (dual of [(514, 17), 8700, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |