Information on Result #679211

Linear OA(4245, 16439, F4, 44) (dual of [16439, 16194, 45]-code), using construction X applied to Ce(44) ⊂ Ce(36) based on
  1. linear OA(4232, 16384, F4, 45) (dual of [16384, 16152, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
  2. 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]
  3. linear OA(413, 55, F4, 6) (dual of [55, 42, 7]-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(4246, 16440, F4, 44) (dual of [16440, 16194, 45]-code) [i]Code Embedding in Larger Space
2Linear OA(4249, 16443, F4, 44) (dual of [16443, 16194, 45]-code) [i]
3Linear OOA(4245, 16439, F4, 2, 44) (dual of [(16439, 2), 32633, 45]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(4245, 16439, F4, 3, 44) (dual of [(16439, 3), 49072, 45]-NRT-code) [i]
5Digital (201, 245, 16439)-net over F4 [i]
6Linear OA(4246, 16441, F4, 44) (dual of [16441, 16195, 45]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OA(4247, 16443, F4, 44) (dual of [16443, 16196, 45]-code) [i]
8Linear OOA(4245, 8219, F4, 2, 44) (dual of [(8219, 2), 16193, 45]-NRT-code) [i]OOA Folding
9Linear OOA(4245, 5479, F4, 3, 44) (dual of [(5479, 3), 16192, 45]-NRT-code) [i]