Information on Result #678319

Linear OA(4116, 262188, F4, 16) (dual of [262188, 262072, 17]-code), using construction X applied to C([0,8]) ⊂ C([0,5]) based on
  1. linear OA(4109, 262145, F4, 17) (dual of [262145, 262036, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
  2. linear OA(473, 262145, F4, 11) (dual of [262145, 262072, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
  3. linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-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(4117, 262189, F4, 16) (dual of [262189, 262072, 17]-code) [i]Code Embedding in Larger Space
2Linear OOA(4116, 177747, F4, 2, 16) (dual of [(177747, 2), 355378, 17]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(4116, 177747, F4, 3, 16) (dual of [(177747, 3), 533125, 17]-NRT-code) [i]
4Digital (100, 116, 177747)-net over F4 [i]
5Linear OA(4118, 262191, F4, 16) (dual of [262191, 262073, 17]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(4116, 131094, F4, 2, 16) (dual of [(131094, 2), 262072, 17]-NRT-code) [i]OOA Folding
7Linear OOA(4116, 87396, F4, 3, 16) (dual of [(87396, 3), 262072, 17]-NRT-code) [i]
8Linear OOA(4116, 32773, F4, 16, 16) (dual of [(32773, 16), 524252, 17]-NRT-code) [i]OA Folding and Stacking