Information on Result #1301798

Linear OA(5124, 78173, F5, 20) (dual of [78173, 78049, 21]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5122, 78169, F5, 20) (dual of [78169, 78047, 21]-code), using
    • construction X applied to Ce(20) ⊂ Ce(13) [i] based on
      1. linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
      2. linear OA(578, 78125, F5, 14) (dual of [78125, 78047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
      3. linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
  2. linear OA(5122, 78171, F5, 19) (dual of [78171, 78049, 20]-code), using Gilbert–VarÅ¡amov bound and bm = 5122 > Vbs−1(k−1) = 127243 541995 582269 712602 769755 424076 618807 471408 522340 486071 431031 453451 727584 655289 [i]
  3. linear OA(50, 2, F5, 0) (dual of [2, 2, 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(5124, 78173, F5, 2, 20) (dual of [(78173, 2), 156222, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5124, 78173, F5, 3, 20) (dual of [(78173, 3), 234395, 21]-NRT-code) [i]
3Digital (104, 124, 78173)-net over F5 [i]
4Linear OOA(5124, 39086, F5, 2, 20) (dual of [(39086, 2), 78048, 21]-NRT-code) [i]OOA Folding