Information on Result #675195

Linear OA(3106, 19716, F3, 17) (dual of [19716, 19610, 18]-code), using construction X applied to Ce(16) ⊂ Ce(12) based on
  1. linear OA(3100, 19683, F3, 17) (dual of [19683, 19583, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  2. linear OA(373, 19683, F3, 13) (dual of [19683, 19610, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  3. linear OA(36, 33, F3, 3) (dual of [33, 27, 4]-code or 33-cap in PG(5,3)), 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(3107, 19717, F3, 17) (dual of [19717, 19610, 18]-code) [i]Code Embedding in Larger Space
2Linear OA(3108, 19718, F3, 17) (dual of [19718, 19610, 18]-code) [i]
3Linear OA(3109, 19719, F3, 17) (dual of [19719, 19610, 18]-code) [i]
4Linear OA(3109, 19720, F3, 17) (dual of [19720, 19611, 18]-code) [i]Construction X with VarÅ¡amov Bound
5Linear OOA(3106, 9858, F3, 2, 17) (dual of [(9858, 2), 19610, 18]-NRT-code) [i]OOA Folding
6Linear OOA(3106, 6572, F3, 3, 17) (dual of [(6572, 3), 19610, 18]-NRT-code) [i]
7Linear OOA(3106, 4929, F3, 4, 17) (dual of [(4929, 4), 19610, 18]-NRT-code) [i]
8Linear OOA(3106, 3943, F3, 5, 17) (dual of [(3943, 5), 19609, 18]-NRT-code) [i]
9Linear OOA(3106, 2464, F3, 17, 17) (dual of [(2464, 17), 41782, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row