Information on Result #679158

Linear OA(4200, 16422, F4, 37) (dual of [16422, 16222, 38]-code), using construction X applied to Ce(36) ⊂ Ce(30) 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(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  3. linear OA(410, 38, F4, 5) (dual of [38, 28, 6]-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(4201, 16423, F4, 37) (dual of [16423, 16222, 38]-code) [i]Code Embedding in Larger Space
2Linear OA(4202, 16424, F4, 37) (dual of [16424, 16222, 38]-code) [i]
3Linear OA(4199, 16421, F4, 36) (dual of [16421, 16222, 37]-code) [i]Truncation
4Linear OOA(4200, 12254, F4, 2, 37) (dual of [(12254, 2), 24308, 38]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(4200, 12254, F4, 3, 37) (dual of [(12254, 3), 36562, 38]-NRT-code) [i]
6Digital (163, 200, 12254)-net over F4 [i]
7Linear OOA(4200, 8211, F4, 2, 37) (dual of [(8211, 2), 16222, 38]-NRT-code) [i]OOA Folding
8Linear OOA(4200, 5474, F4, 3, 37) (dual of [(5474, 3), 16222, 38]-NRT-code) [i]