Information on Result #678777

Linear OA(4193, 65600, F4, 30) (dual of [65600, 65407, 31]-code), using construction X applied to Ce(29) ⊂ Ce(21) based on
  1. linear OA(4177, 65536, F4, 30) (dual of [65536, 65359, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
  2. linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
  3. linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using
    • an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]

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(4194, 65601, F4, 30) (dual of [65601, 65407, 31]-code) [i]Code Embedding in Larger Space
2Linear OA(4195, 65602, F4, 30) (dual of [65602, 65407, 31]-code) [i]
3Linear OOA(4193, 50595, F4, 2, 30) (dual of [(50595, 2), 100997, 31]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(4193, 50595, F4, 3, 30) (dual of [(50595, 3), 151592, 31]-NRT-code) [i]
5Digital (163, 193, 50595)-net over F4 [i]
6Linear OA(4195, 65603, F4, 30) (dual of [65603, 65408, 31]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OOA(4193, 32800, F4, 2, 30) (dual of [(32800, 2), 65407, 31]-NRT-code) [i]OOA Folding
8Linear OOA(4193, 21866, F4, 3, 30) (dual of [(21866, 3), 65405, 31]-NRT-code) [i]
9Linear OOA(4193, 4373, F4, 30, 30) (dual of [(4373, 30), 130997, 31]-NRT-code) [i]OA Folding and Stacking