Information on Result #678747

Linear OA(4251, 65586, F4, 40) (dual of [65586, 65335, 41]-code), using construction X applied to Ce(40) ⊂ Ce(33) based on
  1. linear OA(4241, 65536, F4, 41) (dual of [65536, 65295, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
  2. linear OA(4201, 65536, F4, 34) (dual of [65536, 65335, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
  3. linear OA(410, 50, F4, 5) (dual of [50, 40, 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, 65587, F4, 40) (dual of [65587, 65335, 41]-code) [i]Code Embedding in Larger Space
2Linear OOA(4251, 45742, F4, 2, 40) (dual of [(45742, 2), 91233, 41]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(4251, 45742, F4, 3, 40) (dual of [(45742, 3), 136975, 41]-NRT-code) [i]
4Digital (211, 251, 45742)-net over F4 [i]
5Linear OOA(4251, 32793, F4, 2, 40) (dual of [(32793, 2), 65335, 41]-NRT-code) [i]OOA Folding
6Linear OOA(4251, 21862, F4, 3, 40) (dual of [(21862, 3), 65335, 41]-NRT-code) [i]
7Linear OOA(4251, 3279, F4, 40, 40) (dual of [(3279, 40), 130909, 41]-NRT-code) [i]OA Folding and Stacking