Information on Result #1324308

Linear OA(5131, 390676, F5, 19) (dual of [390676, 390545, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5130, 390674, F5, 19) (dual of [390674, 390544, 20]-code), using
    • construction X applied to Ce(18) ⊂ Ce(12) [i] based on
      1. linear OA(5121, 390625, F5, 19) (dual of [390625, 390504, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(581, 390625, F5, 13) (dual of [390625, 390544, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(59, 49, F5, 5) (dual of [49, 40, 6]-code), using
  2. linear OA(5130, 390675, F5, 18) (dual of [390675, 390545, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 5130 > Vbs−1(k−1) = 5 554583 899118 143196 584302 708100 352978 795203 033577 510806 938574 584992 774560 037859 667709 645273 [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(5131, 390676, F5, 2, 19) (dual of [(390676, 2), 781221, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5131, 390676, F5, 3, 19) (dual of [(390676, 3), 1171897, 20]-NRT-code) [i]
3Digital (112, 131, 390676)-net over F5 [i]
4Linear OOA(5131, 195338, F5, 2, 19) (dual of [(195338, 2), 390545, 20]-NRT-code) [i]OOA Folding