Information on Result #1301257

Linear OA(531, 78136, F5, 6) (dual of [78136, 78105, 7]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(530, 78134, F5, 6) (dual of [78134, 78104, 7]-code), using
    • construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
      1. linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(58, 9, F5, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,5)), using
      4. linear OA(51, 9, F5, 1) (dual of [9, 8, 2]-code), using
  2. linear OA(530, 78135, F5, 5) (dual of [78135, 78105, 6]-code), using Gilbert–VarÅ¡amov bound and bm = 530 > Vbs−1(k−1) = 397 521996 079019 100745 [i]
  3. linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using

Mode: 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(531, 78136, F5, 2, 6) (dual of [(78136, 2), 156241, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(531, 78136, F5, 3, 6) (dual of [(78136, 3), 234377, 7]-NRT-code) [i]
3Digital (25, 31, 78136)-net over F5 [i]
4Linear OOA(531, 39068, F5, 2, 6) (dual of [(39068, 2), 78105, 7]-NRT-code) [i]OOA Folding