Information on Result #1324344

Linear OA(8110, 2097206, F8, 17) (dual of [2097206, 2097096, 18]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8109, 2097204, F8, 17) (dual of [2097204, 2097095, 18]-code), using
    • construction X applied to Ce(16) ⊂ Ce(9) [i] based on
      1. linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
      2. linear OA(857, 2097152, F8, 10) (dual of [2097152, 2097095, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
      3. linear OA(810, 52, F8, 6) (dual of [52, 42, 7]-code), using
  2. linear OA(8109, 2097205, F8, 16) (dual of [2097205, 2097096, 17]-code), using Gilbert–VarÅ¡amov bound and bm = 8109 > Vbs−1(k−1) = 242415 201163 136676 352822 865733 854377 170346 234986 048571 114220 298324 098363 444488 446943 445522 557636 [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(8110, 2097206, F8, 2, 17) (dual of [(2097206, 2), 4194302, 18]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8110, 2097206, F8, 3, 17) (dual of [(2097206, 3), 6291508, 18]-NRT-code) [i]
3Digital (93, 110, 2097206)-net over F8 [i]
4Linear OOA(8110, 1048603, F8, 2, 17) (dual of [(1048603, 2), 2097096, 18]-NRT-code) [i]OOA Folding