Information on Result #1324378

Linear OA(8168, 2097215, F8, 26) (dual of [2097215, 2097047, 27]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8167, 2097213, F8, 26) (dual of [2097213, 2097046, 27]-code), using
    • construction X applied to Ce(25) ⊂ Ce(17) [i] based on
      1. linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(812, 61, F8, 7) (dual of [61, 49, 8]-code), using
  2. linear OA(8167, 2097214, F8, 25) (dual of [2097214, 2097047, 26]-code), using Gilbert–VarÅ¡amov bound and bm = 8167 > Vbs−1(k−1) = 16181 241219 326635 259866 871563 018209 161138 236042 045957 291509 572517 292579 079227 935752 357699 177512 889517 203817 430693 758826 598670 697728 289232 771667 743993 [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(8168, 2097215, F8, 2, 26) (dual of [(2097215, 2), 4194262, 27]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8168, 2097215, F8, 3, 26) (dual of [(2097215, 3), 6291477, 27]-NRT-code) [i]
3Digital (142, 168, 2097215)-net over F8 [i]