Information on Result #1324382

Linear OA(8173, 2097206, F8, 27) (dual of [2097206, 2097033, 28]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8172, 2097204, F8, 27) (dual of [2097204, 2097032, 28]-code), using
    • construction X applied to Ce(26) ⊂ Ce(19) [i] based on
      1. linear OA(8162, 2097152, F8, 27) (dual of [2097152, 2096990, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
      2. linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
      3. linear OA(810, 52, F8, 6) (dual of [52, 42, 7]-code), using
  2. linear OA(8172, 2097205, F8, 26) (dual of [2097205, 2097033, 27]-code), using Gilbert–VarÅ¡amov bound and bm = 8172 > Vbs−1(k−1) = 9500 815193 014620 997069 268746 727933 157413 684673 545155 958853 272828 168507 691871 221601 046024 092865 757511 128287 613836 009924 065728 266684 400524 396964 434189 400892 [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(8173, 2097206, F8, 2, 27) (dual of [(2097206, 2), 4194239, 28]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8173, 2097206, F8, 3, 27) (dual of [(2097206, 3), 6291445, 28]-NRT-code) [i]
3Digital (146, 173, 2097206)-net over F8 [i]
4Linear OOA(8173, 1048603, F8, 2, 27) (dual of [(1048603, 2), 2097033, 28]-NRT-code) [i]OOA Folding