Information on Result #699258

Linear OA(8182, 531468, F81, 26) (dual of [531468, 531386, 27]-code), using construction X applied to Ce(25) ⊂ Ce(18) based on
  1. linear OA(8176, 531441, F81, 26) (dual of [531441, 531365, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
  2. linear OA(8155, 531441, F81, 19) (dual of [531441, 531386, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(8182, 338373, F81, 2, 26) (dual of [(338373, 2), 676664, 27]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8182, 338373, F81, 3, 26) (dual of [(338373, 3), 1015037, 27]-NRT-code) [i]
3Linear OOA(8182, 338373, F81, 4, 26) (dual of [(338373, 4), 1353410, 27]-NRT-code) [i]
4Digital (56, 82, 338373)-net over F81 [i]
5Linear OOA(8182, 265734, F81, 2, 26) (dual of [(265734, 2), 531386, 27]-NRT-code) [i]OOA Folding
6Linear OOA(8182, 177156, F81, 3, 26) (dual of [(177156, 3), 531386, 27]-NRT-code) [i]
7Linear OOA(8182, 132867, F81, 4, 26) (dual of [(132867, 4), 531386, 27]-NRT-code) [i]
8Linear OOA(8182, 40882, F81, 26, 26) (dual of [(40882, 26), 1062850, 27]-NRT-code) [i]OA Folding and Stacking