Information on Result #678767

Linear OA(4131, 65586, F4, 20) (dual of [65586, 65455, 21]-code), using construction X applied to Ce(20) ⊂ Ce(13) based on
  1. linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
  2. linear OA(481, 65536, F4, 14) (dual of [65536, 65455, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(4132, 65587, F4, 20) (dual of [65587, 65455, 21]-code) [i]Code Embedding in Larger Space
2Linear OOA(4131, 56119, F4, 2, 20) (dual of [(56119, 2), 112107, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(4131, 56119, F4, 3, 20) (dual of [(56119, 3), 168226, 21]-NRT-code) [i]
4Digital (111, 131, 56119)-net over F4 [i]
5Linear OA(4133, 65589, F4, 20) (dual of [65589, 65456, 21]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(4131, 32793, F4, 2, 20) (dual of [(32793, 2), 65455, 21]-NRT-code) [i]OOA Folding
7Linear OOA(4131, 21862, F4, 3, 20) (dual of [(21862, 3), 65455, 21]-NRT-code) [i]
8Linear OOA(4131, 6558, F4, 20, 20) (dual of [(6558, 20), 131029, 21]-NRT-code) [i]OA Folding and Stacking