Information on Result #737578

Linear OA(5108, 15666, F5, 21) (dual of [15666, 15558, 22]-code), using construction X applied to Ce(20) ⊂ Ce(13) based on
  1. linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
  2. linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(5110, 15668, F5, 21) (dual of [15668, 15558, 22]-code) [i]Code Embedding in Larger Space
2Linear OOA(5108, 15666, F5, 2, 21) (dual of [(15666, 2), 31224, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(5108, 15666, F5, 3, 21) (dual of [(15666, 3), 46890, 22]-NRT-code) [i]
4Digital (87, 108, 15666)-net over F5 [i]
5Linear OA(5109, 15668, F5, 21) (dual of [15668, 15559, 22]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OA(5110, 15670, F5, 21) (dual of [15670, 15560, 22]-code) [i]
7Linear OOA(5108, 7833, F5, 2, 21) (dual of [(7833, 2), 15558, 22]-NRT-code) [i]OOA Folding
8Linear OOA(5108, 5222, F5, 3, 21) (dual of [(5222, 3), 15558, 22]-NRT-code) [i]
9Linear OOA(5108, 1566, F5, 21, 21) (dual of [(1566, 21), 32778, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row