Information on Result #1301335

Linear OA(551, 390645, F5, 8) (dual of [390645, 390594, 9]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(550, 390643, F5, 8) (dual of [390643, 390593, 9]-code), using
    • construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
      1. linear OA(549, 390625, F5, 8) (dual of [390625, 390576, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
      2. linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
      3. linear OA(517, 18, F5, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,5)), using
      4. linear OA(51, 18, F5, 1) (dual of [18, 17, 2]-code), using
  2. linear OA(550, 390644, F5, 7) (dual of [390644, 390594, 8]-code), using Gilbert–VarÅ¡amov bound and bm = 550 > Vbs−1(k−1) = 20215 883308 592692 005982 117764 712381 [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(551, 390645, F5, 2, 8) (dual of [(390645, 2), 781239, 9]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(551, 390645, F5, 3, 8) (dual of [(390645, 3), 1171884, 9]-NRT-code) [i]
3Digital (43, 51, 390645)-net over F5 [i]