Information on Result #679185

Linear OA(4221, 16429, F4, 40) (dual of [16429, 16208, 41]-code), using construction X applied to Ce(40) ⊂ Ce(33) based on
  1. linear OA(4211, 16384, F4, 41) (dual of [16384, 16173, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
  2. linear OA(4176, 16384, F4, 34) (dual of [16384, 16208, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
  3. linear OA(410, 45, F4, 5) (dual of [45, 35, 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, 16430, F4, 40) (dual of [16430, 16208, 41]-code) [i]Code Embedding in Larger Space
2Linear OOA(4221, 15291, F4, 2, 40) (dual of [(15291, 2), 30361, 41]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(4221, 15291, F4, 3, 40) (dual of [(15291, 3), 45652, 41]-NRT-code) [i]
4Digital (181, 221, 15291)-net over F4 [i]
5Linear OA(4223, 16432, F4, 40) (dual of [16432, 16209, 41]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(4221, 8214, F4, 2, 40) (dual of [(8214, 2), 16207, 41]-NRT-code) [i]OOA Folding
7Linear OOA(4221, 5476, F4, 3, 40) (dual of [(5476, 3), 16207, 41]-NRT-code) [i]