Information on Result #1301919

Linear OA(5144, 78171, F5, 24) (dual of [78171, 78027, 25]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5143, 78169, F5, 24) (dual of [78169, 78026, 25]-code), using
    • construction X applied to Ce(23) ⊂ Ce(17) [i] based on
      1. linear OA(5134, 78125, F5, 24) (dual of [78125, 77991, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
      2. linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
      3. linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
  2. linear OA(5143, 78170, F5, 23) (dual of [78170, 78027, 24]-code), using Gilbert–VarÅ¡amov bound and bm = 5143 > Vbs−1(k−1) = 6919 273567 409189 766648 254455 360624 157019 827266 297742 275837 739085 543480 523758 787164 096345 269203 323685 [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(5144, 78171, F5, 2, 24) (dual of [(78171, 2), 156198, 25]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5144, 78171, F5, 3, 24) (dual of [(78171, 3), 234369, 25]-NRT-code) [i]
3Digital (120, 144, 78171)-net over F5 [i]