Information on Result #699479

Linear OA(8113, 6569, F81, 6) (dual of [6569, 6556, 7]-code), using construction X applied to Ce(5) ⊂ Ce(2) based on
  1. linear OA(8111, 6561, F81, 6) (dual of [6561, 6550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
  2. linear OA(815, 6561, F81, 3) (dual of [6561, 6556, 4]-code or 6561-cap in PG(4,81)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
  3. linear OA(812, 8, F81, 2) (dual of [8, 6, 3]-code or 8-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:

ResultThis
result
only		Method
1Linear OOA(8113, 6569, F81, 2, 6) (dual of [(6569, 2), 13125, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8113, 6569, F81, 3, 6) (dual of [(6569, 3), 19694, 7]-NRT-code) [i]
3Linear OOA(8113, 6569, F81, 4, 6) (dual of [(6569, 4), 26263, 7]-NRT-code) [i]
4Digital (7, 13, 6569)-net over F81 [i]
5Linear OOA(8113, 3284, F81, 2, 6) (dual of [(3284, 2), 6555, 7]-NRT-code) [i]OOA Folding
6Linear OOA(8113, 2189, F81, 3, 6) (dual of [(2189, 3), 6554, 7]-NRT-code) [i]
7Linear OOA(8113, 2189, F81, 4, 6) (dual of [(2189, 4), 8743, 7]-NRT-code) [i]OA Folding and Stacking
8Linear OOA(8113, 2189, F81, 6, 6) (dual of [(2189, 6), 13121, 7]-NRT-code) [i]