Information on Result #699266

Linear OA(8158, 531468, F81, 18) (dual of [531468, 531410, 19]-code), using construction X applied to Ce(17) ⊂ Ce(10) based on
  1. linear OA(8152, 531441, F81, 18) (dual of [531441, 531389, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(8131, 531441, F81, 11) (dual of [531441, 531410, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
  3. linear OA(816, 27, F81, 6) (dual of [27, 21, 7]-code or 27-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(8158, 531468, F81, 2, 18) (dual of [(531468, 2), 1062878, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8158, 531468, F81, 3, 18) (dual of [(531468, 3), 1594346, 19]-NRT-code) [i]
3Linear OOA(8158, 531468, F81, 4, 18) (dual of [(531468, 4), 2125814, 19]-NRT-code) [i]
4Digital (40, 58, 531468)-net over F81 [i]
5Linear OOA(8158, 265734, F81, 2, 18) (dual of [(265734, 2), 531410, 19]-NRT-code) [i]OOA Folding
6Linear OOA(8158, 177156, F81, 3, 18) (dual of [(177156, 3), 531410, 19]-NRT-code) [i]
7Linear OOA(8158, 132867, F81, 4, 18) (dual of [(132867, 4), 531410, 19]-NRT-code) [i]
8Linear OOA(8158, 59052, F81, 18, 18) (dual of [(59052, 18), 1062878, 19]-NRT-code) [i]OA Folding and Stacking