Information on Result #1302038

Linear OA(750, 16827, F7, 11) (dual of [16827, 16777, 12]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(749, 16825, F7, 11) (dual of [16825, 16776, 12]-code), using
    • construction X applied to Ce(10) ⊂ Ce(7) [i] based on
      1. linear OA(746, 16807, F7, 11) (dual of [16807, 16761, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      2. linear OA(731, 16807, F7, 8) (dual of [16807, 16776, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
      3. linear OA(73, 18, F7, 2) (dual of [18, 15, 3]-code), using
  2. linear OA(749, 16826, F7, 10) (dual of [16826, 16777, 11]-code), using Gilbert–VarÅ¡amov bound and bm = 749 > Vbs−1(k−1) = 2994 354468 231915 442866 515084 866976 097991 [i]
  3. linear OA(70, 1, F7, 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(750, 16827, F7, 2, 11) (dual of [(16827, 2), 33604, 12]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(750, 16827, F7, 3, 11) (dual of [(16827, 3), 50431, 12]-NRT-code) [i]
3Digital (39, 50, 16827)-net over F7 [i]