Information on Result #737571

Linear OA(5132, 15666, F5, 26) (dual of [15666, 15534, 27]-code), using construction X applied to Ce(25) ⊂ Ce(18) based on
  1. linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
  2. linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  3. linear OA(511, 41, F5, 6) (dual of [41, 30, 7]-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(5134, 15668, F5, 26) (dual of [15668, 15534, 27]-code) [i]Code Embedding in Larger Space
2Linear OOA(5132, 15666, F5, 2, 26) (dual of [(15666, 2), 31200, 27]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(5132, 15666, F5, 3, 26) (dual of [(15666, 3), 46866, 27]-NRT-code) [i]
4Digital (106, 132, 15666)-net over F5 [i]
5Linear OA(5133, 15668, F5, 26) (dual of [15668, 15535, 27]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OA(5134, 15670, F5, 26) (dual of [15670, 15536, 27]-code) [i]
7Linear OOA(5132, 7833, F5, 2, 26) (dual of [(7833, 2), 15534, 27]-NRT-code) [i]OOA Folding
8Linear OOA(5132, 5222, F5, 3, 26) (dual of [(5222, 3), 15534, 27]-NRT-code) [i]
9Linear OOA(5132, 1205, F5, 26, 26) (dual of [(1205, 26), 31198, 27]-NRT-code) [i]OA Folding and Stacking