Information on Result #1302572

Linear OA(875, 2097178, F8, 12) (dual of [2097178, 2097103, 13]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(874, 2097176, F8, 12) (dual of [2097176, 2097102, 13]-code), using
    • construction X applied to Ce(11) ⊂ Ce(8) [i] based on
      1. linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
      2. linear OA(850, 2097152, F8, 9) (dual of [2097152, 2097102, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      3. linear OA(83, 24, F8, 2) (dual of [24, 21, 3]-code), using
  2. linear OA(874, 2097177, F8, 11) (dual of [2097177, 2097103, 12]-code), using Gilbert–VarÅ¡amov bound and bm = 874 > Vbs−1(k−1) = 128102 361101 264540 908329 698815 640863 772881 568097 645042 242732 791298 [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(875, 2097178, F8, 2, 12) (dual of [(2097178, 2), 4194281, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(875, 2097178, F8, 3, 12) (dual of [(2097178, 3), 6291459, 13]-NRT-code) [i]
3Digital (63, 75, 2097178)-net over F8 [i]
4Linear OOA(875, 1048589, F8, 2, 12) (dual of [(1048589, 2), 2097103, 13]-NRT-code) [i]OOA Folding