Information on Result #698627
Linear OA(6424, 4108, F64, 11) (dual of [4108, 4084, 12]-code), using construction X applied to C([0,5]) ⊂ C([0,3]) based on
- 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(6413, 4097, F64, 7) (dual of [4097, 4084, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(643, 11, F64, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), 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(3229, 4108, S32, 11) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6424, 2714, F64, 2, 11) (dual of [(2714, 2), 5404, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6424, 2714, F64, 3, 11) (dual of [(2714, 3), 8118, 12]-NRT-code) | [i] | ||
| 4 | Digital (13, 24, 2714)-net over F64 | [i] | ||
| 5 | Linear OOA(6424, 2054, F64, 2, 11) (dual of [(2054, 2), 4084, 12]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6424, 1369, F64, 3, 11) (dual of [(1369, 3), 4083, 12]-NRT-code) | [i] | ||
| 7 | Linear OOA(6424, 821, F64, 11, 11) (dual of [(821, 11), 9007, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |