Information on Result #1302720

Linear OA(8108, 2097198, F8, 17) (dual of [2097198, 2097090, 18]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8106, 2097194, F8, 17) (dual of [2097194, 2097088, 18]-code), using
    • construction X applied to Ce(16) ⊂ Ce(10) [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(864, 2097152, F8, 11) (dual of [2097152, 2097088, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      3. linear OA(87, 42, F8, 5) (dual of [42, 35, 6]-code), using
  2. linear OA(8106, 2097196, F8, 16) (dual of [2097196, 2097090, 17]-code), using Gilbert–VarÅ¡amov bound and bm = 8106 > Vbs−1(k−1) = 242399 596970 086351 243054 889726 218444 646027 501575 904216 113648 310799 616879 859753 883161 980522 962720 [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(8108, 2097198, F8, 2, 17) (dual of [(2097198, 2), 4194288, 18]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8108, 2097198, F8, 3, 17) (dual of [(2097198, 3), 6291486, 18]-NRT-code) [i]
3Digital (91, 108, 2097198)-net over F8 [i]
4Linear OOA(8108, 1048599, F8, 2, 17) (dual of [(1048599, 2), 2097090, 18]-NRT-code) [i]OOA Folding