Information on Result #698624
Linear OA(6436, 4108, F64, 17) (dual of [4108, 4072, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,6]) 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(6425, 4097, F64, 13) (dual of [4097, 4072, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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(3244, 4108, S32, 17) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6436, 2054, F64, 2, 17) (dual of [(2054, 2), 4072, 18]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(6436, 1369, F64, 3, 17) (dual of [(1369, 3), 4071, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(6436, 513, F64, 17, 17) (dual of [(513, 17), 8685, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |