Information on Result #1302663

Linear OA(897, 2097186, F8, 15) (dual of [2097186, 2097089, 16]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(896, 2097184, F8, 15) (dual of [2097184, 2097088, 16]-code), using
    • construction X applied to Ce(14) ⊂ Ce(10) [i] based on
      1. linear OA(892, 2097152, F8, 15) (dual of [2097152, 2097060, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
  2. linear OA(896, 2097185, F8, 14) (dual of [2097185, 2097089, 15]-code), using Gilbert–VarÅ¡amov bound and bm = 896 > Vbs−1(k−1) = 236185 591452 016500 685730 772280 819524 172285 244952 021044 518434 930124 849045 910454 772973 [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(897, 2097186, F8, 2, 15) (dual of [(2097186, 2), 4194275, 16]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(897, 2097186, F8, 3, 15) (dual of [(2097186, 3), 6291461, 16]-NRT-code) [i]
3Digital (82, 97, 2097186)-net over F8 [i]
4Linear OOA(897, 1048593, F8, 2, 15) (dual of [(1048593, 2), 2097089, 16]-NRT-code) [i]OOA Folding