Information on Result #1302802

Linear OA(8122, 2097198, F8, 19) (dual of [2097198, 2097076, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8120, 2097194, F8, 19) (dual of [2097194, 2097074, 20]-code), using
    • construction X applied to Ce(18) ⊂ Ce(12) [i] based on
      1. linear OA(8113, 2097152, F8, 19) (dual of [2097152, 2097039, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(87, 42, F8, 5) (dual of [42, 35, 6]-code), using
  2. linear OA(8120, 2097196, F8, 18) (dual of [2097196, 2097076, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 8120 > Vbs−1(k−1) = 192057 086439 886412 353824 913769 018049 553730 874692 028935 348223 522076 067357 745690 548194 639659 369378 502193 103420 [i]
  3. linear OA(80, 2, F8, 0) (dual of [2, 2, 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(8122, 2097198, F8, 2, 19) (dual of [(2097198, 2), 4194274, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8122, 2097198, F8, 3, 19) (dual of [(2097198, 3), 6291472, 20]-NRT-code) [i]
3Digital (103, 122, 2097198)-net over F8 [i]
4Linear OOA(8122, 1048599, F8, 2, 19) (dual of [(1048599, 2), 2097076, 20]-NRT-code) [i]OOA Folding