Information on Result #1301376

Linear OA(559, 78143, F5, 10) (dual of [78143, 78084, 11]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(558, 78141, F5, 10) (dual of [78141, 78083, 11]-code), using
    • construction X4 applied to Ce(10) ⊂ Ce(7) [i] based on
      1. linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      2. linear OA(543, 78125, F5, 8) (dual of [78125, 78082, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
      3. linear OA(515, 16, F5, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,5)), using
      4. linear OA(51, 16, F5, 1) (dual of [16, 15, 2]-code), using
  2. linear OA(558, 78142, F5, 9) (dual of [78142, 78084, 10]-code), using Gilbert–VarÅ¡amov bound and bm = 558 > Vbs−1(k−1) = 2258 637933 317132 278470 620900 305806 471125 [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(559, 78143, F5, 2, 10) (dual of [(78143, 2), 156227, 11]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(559, 78143, F5, 3, 10) (dual of [(78143, 3), 234370, 11]-NRT-code) [i]
3Digital (49, 59, 78143)-net over F5 [i]