Information on Result #1301341

Linear OA(552, 78143, F5, 9) (dual of [78143, 78091, 10]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(551, 78141, F5, 9) (dual of [78141, 78090, 10]-code), using
    • construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
      1. linear OA(550, 78125, F5, 9) (dual of [78125, 78075, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      2. linear OA(536, 78125, F5, 7) (dual of [78125, 78089, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(551, 78142, F5, 8) (dual of [78142, 78091, 9]-code), using Gilbert–VarÅ¡amov bound and bm = 551 > Vbs−1(k−1) = 57814 285860 754353 425429 482563 022805 [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(552, 78143, F5, 2, 9) (dual of [(78143, 2), 156234, 10]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(552, 78143, F5, 3, 9) (dual of [(78143, 3), 234377, 10]-NRT-code) [i]
3Digital (43, 52, 78143)-net over F5 [i]