Information on Result #1302242

Linear OA(787, 117688, F7, 16) (dual of [117688, 117601, 17]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(786, 117686, F7, 16) (dual of [117686, 117600, 17]-code), using
    • construction X applied to Ce(15) ⊂ Ce(9) [i] based on
      1. linear OA(779, 117649, F7, 16) (dual of [117649, 117570, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
      2. linear OA(749, 117649, F7, 10) (dual of [117649, 117600, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
      3. linear OA(77, 37, F7, 5) (dual of [37, 30, 6]-code), using
  2. linear OA(786, 117687, F7, 15) (dual of [117687, 117601, 16]-code), using Gilbert–VarÅ¡amov bound and bm = 786 > Vbs−1(k−1) = 87807 005009 342998 722892 629779 038966 340523 485094 829976 329535 110863 896593 [i]
  3. linear OA(70, 1, F7, 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(787, 117688, F7, 2, 16) (dual of [(117688, 2), 235289, 17]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(787, 117688, F7, 3, 16) (dual of [(117688, 3), 352977, 17]-NRT-code) [i]
3Digital (71, 87, 117688)-net over F7 [i]
4Linear OOA(787, 58844, F7, 2, 16) (dual of [(58844, 2), 117601, 17]-NRT-code) [i]OOA Folding