Information on Result #699560

Linear OA(8143, 6581, F81, 19) (dual of [6581, 6538, 20]-code), using construction X applied to Ce(18) ⊂ Ce(11) based on
  1. linear OA(8137, 6561, F81, 19) (dual of [6561, 6524, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(8123, 6561, F81, 12) (dual of [6561, 6538, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
  3. linear OA(816, 20, F81, 6) (dual of [20, 14, 7]-code or 20-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:

ResultThis
result
only		Method
1Linear OOA(8143, 4648, F81, 2, 19) (dual of [(4648, 2), 9253, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8143, 4648, F81, 3, 19) (dual of [(4648, 3), 13901, 20]-NRT-code) [i]
3Linear OOA(8143, 4648, F81, 4, 19) (dual of [(4648, 4), 18549, 20]-NRT-code) [i]
4Digital (24, 43, 4648)-net over F81 [i]
5Linear OOA(8143, 3290, F81, 2, 19) (dual of [(3290, 2), 6537, 20]-NRT-code) [i]OOA Folding
6Linear OOA(8143, 1645, F81, 4, 19) (dual of [(1645, 4), 6537, 20]-NRT-code) [i]
7Linear OOA(8143, 731, F81, 19, 19) (dual of [(731, 19), 13846, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row