Information on Result #1324366

Linear OA(8159, 2097206, F8, 25) (dual of [2097206, 2097047, 26]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8158, 2097204, F8, 25) (dual of [2097204, 2097046, 26]-code), using
    • construction X applied to Ce(24) ⊂ Ce(17) [i] based on
      1. linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
      2. linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
      3. linear OA(810, 52, F8, 6) (dual of [52, 42, 7]-code), using
  2. linear OA(8158, 2097205, F8, 24) (dual of [2097205, 2097047, 25]-code), using Gilbert–VarÅ¡amov bound and bm = 8158 > Vbs−1(k−1) = 26451 137907 596161 285243 499885 782366 462694 529229 963755 137826 872783 289012 673374 035179 157689 887248 130176 331090 843636 553954 527699 429370 617976 881736 [i]
  3. linear OA(80, 1, F8, 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(8159, 2097206, F8, 2, 25) (dual of [(2097206, 2), 4194253, 26]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8159, 2097206, F8, 3, 25) (dual of [(2097206, 3), 6291459, 26]-NRT-code) [i]
3Digital (134, 159, 2097206)-net over F8 [i]
4Linear OOA(8159, 1048603, F8, 2, 25) (dual of [(1048603, 2), 2097047, 26]-NRT-code) [i]OOA Folding