Information on Result #698623
Linear OA(6440, 4108, F64, 19) (dual of [4108, 4068, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,7]) based on
- linear OA(6437, 4097, F64, 19) (dual of [4097, 4060, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(6429, 4097, F64, 15) (dual of [4097, 4068, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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 | Linear OA(880, 8216, F8, 19) (dual of [8216, 8136, 20]-code) | [i] | Trace Code | |
| 2 | OA(3248, 4108, S32, 19) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(6440, 2054, F64, 2, 19) (dual of [(2054, 2), 4068, 20]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(6440, 1369, F64, 3, 19) (dual of [(1369, 3), 4067, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(6440, 456, F64, 19, 19) (dual of [(456, 19), 8624, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |