Information on Result #1301690

Linear OA(5107, 15662, F5, 21) (dual of [15662, 15555, 22]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5103, 15655, F5, 21) (dual of [15655, 15552, 22]-code), using
    • construction X applied to Ce(20) ⊂ Ce(15) [i] based on
      1. linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
      2. linear OA(573, 15625, F5, 16) (dual of [15625, 15552, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
      3. linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
  2. linear OA(5103, 15658, F5, 19) (dual of [15658, 15555, 20]-code), using Gilbert–VarÅ¡amov bound and bm = 5103 > Vbs−1(k−1) = 33991 648155 809588 076181 086724 730334 880932 325183 587962 436298 912740 804325 [i]
  3. linear OA(51, 4, F5, 1) (dual of [4, 3, 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(5107, 15662, F5, 2, 21) (dual of [(15662, 2), 31217, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5107, 15662, F5, 3, 21) (dual of [(15662, 3), 46879, 22]-NRT-code) [i]
3Digital (86, 107, 15662)-net over F5 [i]
4Linear OOA(5107, 7831, F5, 2, 21) (dual of [(7831, 2), 15555, 22]-NRT-code) [i]OOA Folding