Information on Result #698628
Linear OA(6420, 4108, F64, 9) (dual of [4108, 4088, 10]-code), using construction X applied to C([0,4]) ⊂ C([0,2]) based on
- linear OA(6417, 4097, F64, 9) (dual of [4097, 4080, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(649, 4097, F64, 5) (dual of [4097, 4088, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (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(3224, 4108, S32, 9) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6420, 2054, F64, 2, 9) (dual of [(2054, 2), 4088, 10]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(6420, 1369, F64, 3, 9) (dual of [(1369, 3), 4087, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(6420, 1026, F64, 9, 9) (dual of [(1026, 9), 9214, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |