Information on Result #678986

Linear OA(4227, 16443, F4, 41) (dual of [16443, 16216, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,16]) based on
  1. linear OA(4211, 16385, F4, 41) (dual of [16385, 16174, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
  2. linear OA(4169, 16385, F4, 33) (dual of [16385, 16216, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
  3. linear OA(416, 58, F4, 7) (dual of [58, 42, 8]-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(4227, 16443, F4, 40) (dual of [16443, 16216, 41]-code) [i]Strength Reduction
2Linear OA(4228, 16444, F4, 41) (dual of [16444, 16216, 42]-code) [i]Code Embedding in Larger Space
3Linear OA(4229, 16445, F4, 41) (dual of [16445, 16216, 42]-code) [i]
4Linear OA(4226, 16442, F4, 40) (dual of [16442, 16216, 41]-code) [i]Truncation
5Linear OOA(4227, 15787, F4, 2, 41) (dual of [(15787, 2), 31347, 42]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
6Linear OOA(4227, 15787, F4, 3, 41) (dual of [(15787, 3), 47134, 42]-NRT-code) [i]
7Digital (186, 227, 15787)-net over F4 [i]
8Linear OA(4229, 16446, F4, 41) (dual of [16446, 16217, 42]-code) [i]Construction X with VarÅ¡amov Bound
9Linear OOA(4227, 8221, F4, 2, 41) (dual of [(8221, 2), 16215, 42]-NRT-code) [i]OOA Folding
10Linear OOA(4227, 5481, F4, 3, 41) (dual of [(5481, 3), 16216, 42]-NRT-code) [i]