Information on Result #678571

Linear OA(4203, 65579, F4, 33) (dual of [65579, 65376, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,13]) based on
  1. linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (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(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(4204, 65580, F4, 33) (dual of [65580, 65376, 34]-code) [i]Code Embedding in Larger Space
2Linear OA(4205, 65581, F4, 33) (dual of [65581, 65376, 34]-code) [i]
3Linear OA(4202, 65578, F4, 32) (dual of [65578, 65376, 33]-code) [i]Truncation
4Linear OOA(4203, 34650, F4, 2, 33) (dual of [(34650, 2), 69097, 34]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(4203, 34650, F4, 3, 33) (dual of [(34650, 3), 103747, 34]-NRT-code) [i]
6Digital (170, 203, 34650)-net over F4 [i]
7Linear OOA(4203, 32789, F4, 2, 33) (dual of [(32789, 2), 65375, 34]-NRT-code) [i]OOA Folding
8Linear OOA(4203, 21859, F4, 3, 33) (dual of [(21859, 3), 65374, 34]-NRT-code) [i]