Information on Result #1302315

Linear OA(7100, 823587, F7, 16) (dual of [823587, 823487, 17]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(799, 823585, F7, 16) (dual of [823585, 823486, 17]-code), using
    • construction X applied to Ce(15) ⊂ Ce(9) [i] based on
      1. linear OA(792, 823543, F7, 16) (dual of [823543, 823451, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
      2. linear OA(757, 823543, F7, 10) (dual of [823543, 823486, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
      3. linear OA(77, 42, F7, 5) (dual of [42, 35, 6]-code), using
  2. linear OA(799, 823586, F7, 15) (dual of [823586, 823487, 16]-code), using Gilbert–VarÅ¡amov bound and bm = 799 > Vbs−1(k−1) = 59371 824060 408616 172609 415074 459024 267183 670803 108891 412435 509686 674427 305501 787399 [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(7100, 823587, F7, 2, 16) (dual of [(823587, 2), 1647074, 17]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(7100, 823587, F7, 3, 16) (dual of [(823587, 3), 2470661, 17]-NRT-code) [i]
3Digital (84, 100, 823587)-net over F7 [i]