Information on Result #699495

Linear OA(8122, 6572, F81, 10) (dual of [6572, 6550, 11]-code), using construction X applied to Ce(9) ⊂ Ce(5) based on
  1. linear OA(8119, 6561, F81, 10) (dual of [6561, 6542, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
  2. 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]
  3. linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), 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(8122, 4809, F81, 2, 10) (dual of [(4809, 2), 9596, 11]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8122, 4809, F81, 3, 10) (dual of [(4809, 3), 14405, 11]-NRT-code) [i]
3Linear OOA(8122, 4809, F81, 4, 10) (dual of [(4809, 4), 19214, 11]-NRT-code) [i]
4Digital (12, 22, 4809)-net over F81 [i]
5Linear OOA(8122, 3286, F81, 2, 10) (dual of [(3286, 2), 6550, 11]-NRT-code) [i]OOA Folding
6Linear OOA(8122, 2190, F81, 3, 10) (dual of [(2190, 3), 6548, 11]-NRT-code) [i]
7Linear OOA(8122, 1643, F81, 4, 10) (dual of [(1643, 4), 6550, 11]-NRT-code) [i]
8Linear OOA(8122, 1314, F81, 10, 10) (dual of [(1314, 10), 13118, 11]-NRT-code) [i]OA Folding and Stacking