Information on Result #1324318

Linear OA(5135, 390690, F5, 19) (dual of [390690, 390555, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5134, 390688, F5, 19) (dual of [390688, 390554, 20]-code), using
    • construction X applied to Ce(18) ⊂ Ce(10) [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(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(513, 63, F5, 7) (dual of [63, 50, 8]-code), using
  2. linear OA(5134, 390689, F5, 18) (dual of [390689, 390555, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 5134 > Vbs−1(k−1) = 5 557968 808967 153612 590154 441019 132304 614669 591112 820150 441706 838033 788159 645704 545619 679105 [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(5135, 390690, F5, 2, 19) (dual of [(390690, 2), 781245, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5135, 390690, F5, 3, 19) (dual of [(390690, 3), 1171935, 20]-NRT-code) [i]
3Digital (116, 135, 390690)-net over F5 [i]
4Linear OOA(5135, 195345, F5, 2, 19) (dual of [(195345, 2), 390555, 20]-NRT-code) [i]OOA Folding