Information on Result #1324324

Linear OA(5140, 390678, F5, 20) (dual of [390678, 390538, 21]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5138, 390674, F5, 20) (dual of [390674, 390536, 21]-code), using
    • construction X applied to Ce(20) ⊂ Ce(13) [i] based on
      1. linear OA(5129, 390625, F5, 21) (dual of [390625, 390496, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
      2. linear OA(589, 390625, F5, 14) (dual of [390625, 390536, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
      3. linear OA(59, 49, F5, 5) (dual of [49, 40, 6]-code), using
  2. linear OA(5138, 390676, F5, 19) (dual of [390676, 390538, 20]-code), using Gilbert–VarÅ¡amov bound and bm = 5138 > Vbs−1(k−1) = 482230 767446 553790 599437 298807 929627 000981 908075 478799 491572 899511 496574 767658 099330 691930 855741 [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(5140, 390678, F5, 2, 20) (dual of [(390678, 2), 781216, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5140, 390678, F5, 3, 20) (dual of [(390678, 3), 1171894, 21]-NRT-code) [i]
3Digital (120, 140, 390678)-net over F5 [i]
4Linear OOA(5140, 195339, F5, 2, 20) (dual of [(195339, 2), 390538, 21]-NRT-code) [i]OOA Folding