Information on Result #1301819

Linear OA(5126, 390687, F5, 18) (dual of [390687, 390561, 19]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5125, 390685, F5, 18) (dual of [390685, 390560, 19]-code), using
    • construction X applied to Ce(17) ⊂ Ce(10) [i] based on
      1. linear OA(5113, 390625, F5, 18) (dual of [390625, 390512, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
      2. linear OA(565, 390625, F5, 11) (dual of [390625, 390560, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      3. linear OA(512, 60, F5, 6) (dual of [60, 48, 7]-code), using
  2. linear OA(5125, 390686, F5, 17) (dual of [390686, 390561, 18]-code), using Gilbert–VarÅ¡amov bound and bm = 5125 > Vbs−1(k−1) = 60 455958 735334 502993 880184 891632 011854 498948 569514 196087 722235 075298 406401 318037 030485 [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(5126, 390687, F5, 2, 18) (dual of [(390687, 2), 781248, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5126, 390687, F5, 3, 18) (dual of [(390687, 3), 1171935, 19]-NRT-code) [i]
3Digital (108, 126, 390687)-net over F5 [i]