Information on Result #699453
Linear OA(8165, 6569, F81, 32) (dual of [6569, 6504, 33]-code), using construction X applied to Ce(31) ⊂ Ce(28) 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(8157, 6561, F81, 29) (dual of [6561, 6504, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(812, 8, F81, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), 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(9130, 13138, F9, 32) (dual of [13138, 13008, 33]-code) | [i] | Trace Code | |
| 2 | OA(2787, 6569, S27, 32) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(8165, 3284, F81, 2, 32) (dual of [(3284, 2), 6503, 33]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(8165, 2189, F81, 3, 32) (dual of [(2189, 3), 6502, 33]-NRT-code) | [i] | ||
| 5 | Linear OOA(8165, 1642, F81, 4, 32) (dual of [(1642, 4), 6503, 33]-NRT-code) | [i] | ||