Information on Result #699548
Linear OA(8167, 6581, F81, 31) (dual of [6581, 6514, 32]-code), using construction X applied to Ce(30) ⊂ Ce(23) based on
- linear OA(8161, 6561, F81, 31) (dual of [6561, 6500, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(8147, 6561, F81, 24) (dual of [6561, 6514, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(816, 20, F81, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,81)), using
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), using
- Reed–Solomon code RS(75,81) [i]
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), 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(9134, 13162, F9, 31) (dual of [13162, 13028, 32]-code) | [i] | Trace Code | |
| 2 | Linear OOA(8167, 3290, F81, 2, 31) (dual of [(3290, 2), 6513, 32]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8167, 1645, F81, 4, 31) (dual of [(1645, 4), 6513, 32]-NRT-code) | [i] | ||