Information on Result #678032

Linear OA(4143, 4194368, F4, 16) (dual of [4194368, 4194225, 17]-code), using construction X applied to Ce(16) ⊂ Ce(9) based on
  1. linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  2. linear OA(478, 4194304, F4, 10) (dual of [4194304, 4194226, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
  3. linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using
    • an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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 OOA(4143, 2575984, F4, 2, 16) (dual of [(2575984, 2), 5151825, 17]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4143, 2575984, F4, 3, 16) (dual of [(2575984, 3), 7727809, 17]-NRT-code) [i]
3Digital (127, 143, 2575984)-net over F4 [i]
4Linear OOA(4143, 2097184, F4, 2, 16) (dual of [(2097184, 2), 4194225, 17]-NRT-code) [i]OOA Folding
5Linear OOA(4143, 1398122, F4, 3, 16) (dual of [(1398122, 3), 4194223, 17]-NRT-code) [i]
6Linear OOA(4143, 524296, F4, 16, 16) (dual of [(524296, 16), 8388593, 17]-NRT-code) [i]OA Folding and Stacking