Information on Result #678944

Linear OA(4221, 16423, F4, 41) (dual of [16423, 16202, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,17]) 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(4183, 16385, F4, 35) (dual of [16385, 16202, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (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(4222, 16424, F4, 41) (dual of [16424, 16202, 42]-code) [i]Code Embedding in Larger Space
2Linear OA(4223, 16425, F4, 41) (dual of [16425, 16202, 42]-code) [i]
3Linear OA(4220, 16422, F4, 40) (dual of [16422, 16202, 41]-code) [i]Truncation
4Linear OOA(4221, 12749, F4, 2, 41) (dual of [(12749, 2), 25277, 42]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(4221, 12749, F4, 3, 41) (dual of [(12749, 3), 38026, 42]-NRT-code) [i]
6Digital (180, 221, 12749)-net over F4 [i]
7Linear OOA(4221, 8211, F4, 2, 41) (dual of [(8211, 2), 16201, 42]-NRT-code) [i]OOA Folding
8Linear OOA(4221, 5474, F4, 3, 41) (dual of [(5474, 3), 16201, 42]-NRT-code) [i]