Information on Result #698662
Linear OA(6478, 4126, F64, 35) (dual of [4126, 4048, 36]-code), using construction X applied to C([0,17]) ⊂ C([0,12]) based on
- linear OA(6469, 4097, F64, 35) (dual of [4097, 4028, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(6449, 4097, F64, 25) (dual of [4097, 4048, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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(3294, 4126, S32, 35) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6478, 3407, F64, 2, 35) (dual of [(3407, 2), 6736, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6478, 3407, F64, 3, 35) (dual of [(3407, 3), 10143, 36]-NRT-code) | [i] | ||
| 4 | Digital (43, 78, 3407)-net over F64 | [i] | ||
| 5 | Linear OOA(6478, 2063, F64, 2, 35) (dual of [(2063, 2), 4048, 36]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6478, 1375, F64, 3, 35) (dual of [(1375, 3), 4047, 36]-NRT-code) | [i] | ||