Information on Result #699484
Linear OA(8166, 6572, F81, 32) (dual of [6572, 6506, 33]-code), using construction X applied to Ce(31) ⊂ Ce(27) based on
- linear OA(8163, 6561, F81, 32) (dual of [6561, 6498, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(8155, 6561, F81, 28) (dual of [6561, 6506, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), 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(9132, 13144, F9, 32) (dual of [13144, 13012, 33]-code) | [i] | Trace Code | |
| 2 | OA(2788, 6572, S27, 32) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(8166, 3286, F81, 2, 32) (dual of [(3286, 2), 6506, 33]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(8166, 2190, F81, 3, 32) (dual of [(2190, 3), 6504, 33]-NRT-code) | [i] | ||
| 5 | Linear OOA(8166, 1643, F81, 4, 32) (dual of [(1643, 4), 6506, 33]-NRT-code) | [i] | ||