Information on Result #1301519

Linear OA(583, 15662, F5, 16) (dual of [15662, 15579, 17]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(579, 15655, F5, 16) (dual of [15655, 15576, 17]-code), using
    • construction X applied to Ce(15) ⊂ Ce(10) [i] based on
      1. 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]
      2. linear OA(549, 15625, F5, 11) (dual of [15625, 15576, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      3. linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
  2. linear OA(579, 15658, F5, 14) (dual of [15658, 15579, 15]-code), using Gilbert–VarÅ¡amov bound and bm = 579 > Vbs−1(k−1) = 36444 905124 286882 983875 522980 917687 265790 301589 341925 [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(583, 15662, F5, 2, 16) (dual of [(15662, 2), 31241, 17]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(583, 15662, F5, 3, 16) (dual of [(15662, 3), 46903, 17]-NRT-code) [i]
3Digital (67, 83, 15662)-net over F5 [i]
4Linear OOA(583, 7831, F5, 2, 16) (dual of [(7831, 2), 15579, 17]-NRT-code) [i]OOA Folding