Information on Result #678594

Linear OA(4225, 65601, F4, 35) (dual of [65601, 65376, 36]-code), using construction X applied to C([0,17]) ⊂ C([0,13]) based on
  1. 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]
  2. linear OA(4161, 65537, F4, 27) (dual of [65537, 65376, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
  3. linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using
    • an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]

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(4226, 65602, F4, 35) (dual of [65602, 65376, 36]-code) [i]Code Embedding in Larger Space
2Linear OA(4227, 65603, F4, 35) (dual of [65603, 65376, 36]-code) [i]
3Linear OA(4227, 65604, F4, 35) (dual of [65604, 65377, 36]-code) [i]Construction X with VarÅ¡amov Bound
4Linear OA(4228, 65606, F4, 35) (dual of [65606, 65378, 36]-code) [i]
5Linear OOA(4225, 32800, F4, 2, 35) (dual of [(32800, 2), 65375, 36]-NRT-code) [i]OOA Folding
6Linear OOA(4225, 21867, F4, 3, 35) (dual of [(21867, 3), 65376, 36]-NRT-code) [i]