Information on Result #699219

Linear OA(8127, 531452, F81, 9) (dual of [531452, 531425, 10]-code), using construction X applied to Ce(8) ⊂ Ce(5) based on
  1. linear OA(8125, 531441, F81, 9) (dual of [531441, 531416, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
  2. linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
  3. linear OA(812, 11, F81, 2) (dual of [11, 9, 3]-code or 11-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 OA(954, 1062904, F9, 9) (dual of [1062904, 1062850, 10]-code) [i]Trace Code
2Linear OOA(8127, 518185, F81, 2, 9) (dual of [(518185, 2), 1036343, 10]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(8127, 518185, F81, 3, 9) (dual of [(518185, 3), 1554528, 10]-NRT-code) [i]
4Linear OOA(8127, 518185, F81, 4, 9) (dual of [(518185, 4), 2072713, 10]-NRT-code) [i]
5Digital (18, 27, 518185)-net over F81 [i]
6Linear OOA(8127, 265726, F81, 2, 9) (dual of [(265726, 2), 531425, 10]-NRT-code) [i]OOA Folding
7Linear OOA(8127, 177150, F81, 3, 9) (dual of [(177150, 3), 531423, 10]-NRT-code) [i]
8Linear OOA(8127, 132863, F81, 4, 9) (dual of [(132863, 4), 531425, 10]-NRT-code) [i]