Information on Result #678252

Linear OA(4161, 1048636, F4, 20) (dual of [1048636, 1048475, 21]-code), using construction X applied to Ce(20) ⊂ Ce(13) based on
  1. linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
  2. linear OA(4101, 1048576, F4, 14) (dual of [1048576, 1048475, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
  3. linear OA(410, 60, F4, 5) (dual of [60, 50, 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(4162, 1048637, F4, 20) (dual of [1048637, 1048475, 21]-code) [i]Code Embedding in Larger Space
2Linear OOA(4161, 565773, F4, 2, 20) (dual of [(565773, 2), 1131385, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(4161, 565773, F4, 3, 20) (dual of [(565773, 3), 1697158, 21]-NRT-code) [i]
4Digital (141, 161, 565773)-net over F4 [i]
5Linear OA(4163, 1048639, F4, 20) (dual of [1048639, 1048476, 21]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(4161, 524318, F4, 2, 20) (dual of [(524318, 2), 1048475, 21]-NRT-code) [i]OOA Folding
7Linear OOA(4161, 349545, F4, 3, 20) (dual of [(349545, 3), 1048474, 21]-NRT-code) [i]
8Linear OOA(4161, 104863, F4, 20, 20) (dual of [(104863, 20), 2097099, 21]-NRT-code) [i]OA Folding and Stacking