Information on Result #678969

Linear OA(4137, 16423, F4, 25) (dual of [16423, 16286, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,9]) based on
  1. linear OA(4127, 16385, F4, 25) (dual of [16385, 16258, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
  2. linear OA(499, 16385, F4, 19) (dual of [16385, 16286, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [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(4138, 16424, F4, 25) (dual of [16424, 16286, 26]-code) [i]Code Embedding in Larger Space
2Linear OA(4139, 16425, F4, 25) (dual of [16425, 16286, 26]-code) [i]
3Linear OA(4136, 16422, F4, 24) (dual of [16422, 16286, 25]-code) [i]Truncation
4Linear OOA(4137, 11393, F4, 2, 25) (dual of [(11393, 2), 22649, 26]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(4137, 11393, F4, 3, 25) (dual of [(11393, 3), 34042, 26]-NRT-code) [i]
6Digital (112, 137, 11393)-net over F4 [i]
7Linear OA(4139, 16426, F4, 25) (dual of [16426, 16287, 26]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OOA(4137, 8211, F4, 2, 25) (dual of [(8211, 2), 16285, 26]-NRT-code) [i]OOA Folding
9Linear OOA(4137, 5474, F4, 3, 25) (dual of [(5474, 3), 16285, 26]-NRT-code) [i]