Information on Result #1324352

Linear OA(8131, 2097206, F8, 20) (dual of [2097206, 2097075, 21]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8130, 2097204, F8, 20) (dual of [2097204, 2097074, 21]-code), using
    • construction X applied to Ce(19) ⊂ Ce(12) [i] based on
      1. 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]
      2. linear OA(878, 2097152, F8, 13) (dual of [2097152, 2097074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(810, 52, F8, 6) (dual of [52, 42, 7]-code), using
  2. linear OA(8130, 2097205, F8, 19) (dual of [2097205, 2097075, 20]-code), using Gilbert–VarÅ¡amov bound and bm = 8130 > Vbs−1(k−1) = 156647 959268 757393 970832 224016 551798 694116 660876 402554 008840 413423 153447 275124 365442 618148 709321 930411 359550 299821 [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(8131, 2097206, F8, 2, 20) (dual of [(2097206, 2), 4194281, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8131, 2097206, F8, 3, 20) (dual of [(2097206, 3), 6291487, 21]-NRT-code) [i]
3Digital (111, 131, 2097206)-net over F8 [i]
4Linear OOA(8131, 1048603, F8, 2, 20) (dual of [(1048603, 2), 2097075, 21]-NRT-code) [i]OOA Folding