Information on Result #1301844

Linear OA(5132, 78174, F5, 22) (dual of [78174, 78042, 23]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5129, 78169, F5, 22) (dual of [78169, 78040, 23]-code), using
    • construction X applied to Ce(21) ⊂ Ce(15) [i] based on
      1. linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
      2. linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
      3. linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
  2. linear OA(5129, 78171, F5, 20) (dual of [78171, 78042, 21]-code), using Gilbert–VarÅ¡amov bound and bm = 5129 > Vbs−1(k−1) = 2093 551392 438519 134033 978849 958649 341280 527566 061387 058850 326452 192060 758815 302799 882169 [i]
  3. linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-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(5132, 78174, F5, 2, 22) (dual of [(78174, 2), 156216, 23]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5132, 78174, F5, 3, 22) (dual of [(78174, 3), 234390, 23]-NRT-code) [i]
3Digital (110, 132, 78174)-net over F5 [i]
4Linear OOA(5132, 39087, F5, 2, 22) (dual of [(39087, 2), 78042, 23]-NRT-code) [i]OOA Folding