Information on Result #679215

Linear OA(4206, 16442, F4, 37) (dual of [16442, 16236, 38]-code), using construction X applied to Ce(36) ⊂ Ce(28) based on
  1. linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
  2. linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
  3. linear OA(416, 58, F4, 7) (dual of [58, 42, 8]-code), using

Mode: Constructive and 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 OA(4206, 16442, F4, 36) (dual of [16442, 16236, 37]-code) [i]Strength Reduction
2Linear OA(4207, 16443, F4, 37) (dual of [16443, 16236, 38]-code) [i]Code Embedding in Larger Space
3Linear OA(4208, 16444, F4, 37) (dual of [16444, 16236, 38]-code) [i]
4Linear OA(4205, 16441, F4, 36) (dual of [16441, 16236, 37]-code) [i]Truncation
5Linear OOA(4206, 15549, F4, 2, 37) (dual of [(15549, 2), 30892, 38]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
6Linear OOA(4206, 15549, F4, 3, 37) (dual of [(15549, 3), 46441, 38]-NRT-code) [i]
7Digital (169, 206, 15549)-net over F4 [i]
8Linear OA(4208, 16445, F4, 37) (dual of [16445, 16237, 38]-code) [i]Construction X with VarÅ¡amov Bound
9Linear OOA(4206, 8221, F4, 2, 37) (dual of [(8221, 2), 16236, 38]-NRT-code) [i]OOA Folding
10Linear OOA(4206, 5480, F4, 3, 37) (dual of [(5480, 3), 16234, 38]-NRT-code) [i]