Information on Result #699121
Linear OA(8114, 531450, F81, 5) (dual of [531450, 531436, 6]-code), using construction X4 applied to C([0,2]) ⊂ C([0,1]) based on
- linear OA(8113, 531442, F81, 5) (dual of [531442, 531429, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(817, 531442, F81, 3) (dual of [531442, 531435, 4]-code or 531442-cap in PG(6,81)), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(817, 8, F81, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,81)), using
- dual of repetition code with length 8 [i]
- linear OA(811, 8, F81, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 81, F81, 1) (dual of [81, 80, 2]-code), using
- Reed–Solomon code RS(80,81) [i]
- discarding factors / shortening the dual code based on linear OA(811, 81, F81, 1) (dual of [81, 80, 2]-code), 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(928, 1062900, F9, 5) (dual of [1062900, 1062872, 6]-code) | [i] | Trace Code | |
| 2 | Linear OOA(8114, 531450, F81, 2, 5) (dual of [(531450, 2), 1062886, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8114, 531450, F81, 3, 5) (dual of [(531450, 3), 1594336, 6]-NRT-code) | [i] | ||
| 4 | Linear OOA(8114, 531450, F81, 4, 5) (dual of [(531450, 4), 2125786, 6]-NRT-code) | [i] | ||
| 5 | Linear OOA(8114, 265725, F81, 2, 5) (dual of [(265725, 2), 531436, 6]-NRT-code) | [i] | OOA Folding | |