Information on Result #698811

Linear OA(6417, 4104, F64, 8) (dual of [4104, 4087, 9]-code), using construction X applied to Ce(7) ⊂ Ce(4) based on
  1. linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
  2. linear OA(649, 4096, F64, 5) (dual of [4096, 4087, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
  3. linear OA(642, 8, F64, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,64)), 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(834, 8208, F8, 8) (dual of [8208, 8174, 9]-code) [i]Trace Code
2OA(3221, 4104, S32, 8) [i]Discarding Parts of the Base for OAs
3Linear OOA(6417, 3112, F64, 2, 8) (dual of [(3112, 2), 6207, 9]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(6417, 3112, F64, 3, 8) (dual of [(3112, 3), 9319, 9]-NRT-code) [i]
5Digital (9, 17, 3112)-net over F64 [i]
6Linear OOA(6417, 2052, F64, 2, 8) (dual of [(2052, 2), 4087, 9]-NRT-code) [i]OOA Folding
7Linear OOA(6417, 1368, F64, 3, 8) (dual of [(1368, 3), 4087, 9]-NRT-code) [i]
8Linear OOA(6417, 1026, F64, 8, 8) (dual of [(1026, 8), 8191, 9]-NRT-code) [i]OA Folding and Stacking