Information on Result #699601

Linear OA(8168, 6590, F81, 30) (dual of [6590, 6522, 31]-code), using construction X applied to Ce(29) ⊂ Ce(19) based on
  1. linear OA(8159, 6561, F81, 30) (dual of [6561, 6502, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
  2. linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
  3. linear OA(819, 29, F81, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,81)), 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:

ResultThis
result
only
Method
1Linear OOA(8168, 5195, F81, 2, 30) (dual of [(5195, 2), 10322, 31]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8168, 5195, F81, 3, 30) (dual of [(5195, 3), 15517, 31]-NRT-code) [i]
3Linear OOA(8168, 5195, F81, 4, 30) (dual of [(5195, 4), 20712, 31]-NRT-code) [i]
4Digital (38, 68, 5195)-net over F81 [i]
5Linear OOA(8168, 3295, F81, 2, 30) (dual of [(3295, 2), 6522, 31]-NRT-code) [i]OOA Folding
6Linear OOA(8168, 2196, F81, 3, 30) (dual of [(2196, 3), 6520, 31]-NRT-code) [i]
7Linear OOA(8168, 1647, F81, 4, 30) (dual of [(1647, 4), 6520, 31]-NRT-code) [i]