Information on Result #1301884

Linear OA(5138, 78172, F5, 23) (dual of [78172, 78034, 24]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5136, 78169, F5, 23) (dual of [78169, 78033, 24]-code), using
    • construction X applied to Ce(22) ⊂ Ce(16) [i] based on
      1. linear OA(5127, 78125, F5, 23) (dual of [78125, 77998, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
      2. linear OA(592, 78125, F5, 17) (dual of [78125, 78033, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
      3. linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
  2. linear OA(5136, 78170, F5, 21) (dual of [78170, 78034, 22]-code), using Gilbert–VarÅ¡amov bound and bm = 5136 > Vbs−1(k−1) = 32 714359 513332 999726 313542 034775 151021 407241 742771 897852 108779 094423 408600 157540 183212 247845 [i]
  3. linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-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(5138, 78172, F5, 2, 23) (dual of [(78172, 2), 156206, 24]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5138, 78172, F5, 3, 23) (dual of [(78172, 3), 234378, 24]-NRT-code) [i]
3Digital (115, 138, 78172)-net over F5 [i]
4Linear OOA(5138, 39086, F5, 2, 23) (dual of [(39086, 2), 78034, 24]-NRT-code) [i]OOA Folding