Information on Result #699279

Linear OA(8172, 531476, F81, 22) (dual of [531476, 531404, 23]-code), using construction X applied to Ce(21) ⊂ Ce(12) based on
  1. linear OA(8164, 531441, F81, 22) (dual of [531441, 531377, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
  2. linear OA(8137, 531441, F81, 13) (dual of [531441, 531404, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  3. linear OA(818, 35, F81, 8) (dual of [35, 27, 9]-code or 35-arc in PG(7,81)), 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(8172, 531476, F81, 2, 22) (dual of [(531476, 2), 1062880, 23]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8172, 531476, F81, 3, 22) (dual of [(531476, 3), 1594356, 23]-NRT-code) [i]
3Linear OOA(8172, 531476, F81, 4, 22) (dual of [(531476, 4), 2125832, 23]-NRT-code) [i]
4Digital (50, 72, 531476)-net over F81 [i]
5Linear OOA(8172, 265738, F81, 2, 22) (dual of [(265738, 2), 531404, 23]-NRT-code) [i]OOA Folding
6Linear OOA(8172, 177158, F81, 3, 22) (dual of [(177158, 3), 531402, 23]-NRT-code) [i]
7Linear OOA(8172, 132869, F81, 4, 22) (dual of [(132869, 4), 531404, 23]-NRT-code) [i]
8Linear OOA(8172, 48316, F81, 22, 22) (dual of [(48316, 22), 1062880, 23]-NRT-code) [i]OA Folding and Stacking