Information on Result #682569

Linear OA(548, 78152, F5, 8) (dual of [78152, 78104, 9]-code), using construction XX applied to Ce(7) ⊂ Ce(3) ⊂ Ce(2) based on
  1. linear OA(543, 78125, F5, 8) (dual of [78125, 78082, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
  2. linear OA(522, 78125, F5, 4) (dual of [78125, 78103, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
  3. linear OA(515, 78125, F5, 3) (dual of [78125, 78110, 4]-code or 78125-cap in PG(14,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
  4. linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
  5. linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), 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(548, 78152, F5, 2, 8) (dual of [(78152, 2), 156256, 9]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(548, 78152, F5, 3, 8) (dual of [(78152, 3), 234408, 9]-NRT-code) [i]
3Digital (40, 48, 78152)-net over F5 [i]
4Linear OOA(548, 39076, F5, 2, 8) (dual of [(39076, 2), 78104, 9]-NRT-code) [i]OOA Folding
5Linear OOA(548, 19538, F5, 8, 8) (dual of [(19538, 8), 156256, 9]-NRT-code) [i]OA Folding and Stacking