Information on Result #1301725

Linear OA(5109, 78171, F5, 18) (dual of [78171, 78062, 19]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5108, 78169, F5, 18) (dual of [78169, 78061, 19]-code), using
    • construction X applied to Ce(17) ⊂ Ce(11) [i] based on
      1. 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]
      2. linear OA(564, 78125, F5, 12) (dual of [78125, 78061, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
      3. linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
  2. linear OA(5108, 78170, F5, 17) (dual of [78170, 78062, 18]-code), using Gilbert–VarÅ¡amov bound and bm = 5108 > Vbs−1(k−1) = 398 335166 406147 712073 538102 780263 876458 188250 106232 251485 107505 120840 993573 [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(5109, 78171, F5, 2, 18) (dual of [(78171, 2), 156233, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5109, 78171, F5, 3, 18) (dual of [(78171, 3), 234404, 19]-NRT-code) [i]
3Digital (91, 109, 78171)-net over F5 [i]