Information on Result #678563

Linear OA(4251, 65579, F4, 41) (dual of [65579, 65328, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,17]) based on
  1. linear OA(4241, 65537, F4, 41) (dual of [65537, 65296, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
  2. linear OA(4209, 65537, F4, 35) (dual of [65537, 65328, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
  3. linear OA(410, 42, F4, 5) (dual of [42, 32, 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(4252, 65580, F4, 41) (dual of [65580, 65328, 42]-code) [i]Code Embedding in Larger Space
2Linear OA(4253, 65581, F4, 41) (dual of [65581, 65328, 42]-code) [i]
3Linear OA(4250, 65578, F4, 40) (dual of [65578, 65328, 41]-code) [i]Truncation
4Linear OOA(4251, 37093, F4, 2, 41) (dual of [(37093, 2), 73935, 42]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(4251, 37093, F4, 3, 41) (dual of [(37093, 3), 111028, 42]-NRT-code) [i]
6Digital (210, 251, 37093)-net over F4 [i]
7Linear OOA(4251, 32789, F4, 2, 41) (dual of [(32789, 2), 65327, 42]-NRT-code) [i]OOA Folding
8Linear OOA(4251, 21859, F4, 3, 41) (dual of [(21859, 3), 65326, 42]-NRT-code) [i]