Information on Result #1302142

Linear OA(769, 823571, F7, 11) (dual of [823571, 823502, 12]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(767, 823567, F7, 11) (dual of [823567, 823500, 12]-code), using
    • construction X applied to Ce(10) ⊂ Ce(7) [i] based on
      1. linear OA(764, 823543, F7, 11) (dual of [823543, 823479, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      2. linear OA(743, 823543, F7, 8) (dual of [823543, 823500, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
      3. linear OA(73, 24, F7, 2) (dual of [24, 21, 3]-code), using
  2. linear OA(767, 823569, F7, 10) (dual of [823569, 823502, 11]-code), using Gilbert–VarÅ¡amov bound and bm = 767 > Vbs−1(k−1) = 4 840332 546789 490830 563781 026182 561747 581262 573858 747777 [i]
  3. linear OA(70, 2, F7, 0) (dual of [2, 2, 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(769, 823571, F7, 2, 11) (dual of [(823571, 2), 1647073, 12]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(769, 823571, F7, 3, 11) (dual of [(823571, 3), 2470644, 12]-NRT-code) [i]
3Digital (58, 69, 823571)-net over F7 [i]