Information on Result #736961

Linear OA(3197, 19753, F3, 30) (dual of [19753, 19556, 31]-code), using construction X applied to Ce(30) ⊂ Ce(21) based on
  1. linear OA(3181, 19683, F3, 31) (dual of [19683, 19502, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  2. linear OA(3127, 19683, F3, 22) (dual of [19683, 19556, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
  3. linear OA(316, 70, F3, 7) (dual of [70, 54, 8]-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(3199, 19755, F3, 30) (dual of [19755, 19556, 31]-code) [i]Code Embedding in Larger Space
2Linear OOA(3197, 12328, F3, 2, 30) (dual of [(12328, 2), 24459, 31]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(3197, 12328, F3, 3, 30) (dual of [(12328, 3), 36787, 31]-NRT-code) [i]
4Linear OOA(3197, 12328, F3, 4, 30) (dual of [(12328, 4), 49115, 31]-NRT-code) [i]
5Linear OOA(3197, 12328, F3, 5, 30) (dual of [(12328, 5), 61443, 31]-NRT-code) [i]
6Digital (167, 197, 12328)-net over F3 [i]
7Linear OOA(3197, 9876, F3, 2, 30) (dual of [(9876, 2), 19555, 31]-NRT-code) [i]OOA Folding
8Linear OOA(3197, 6584, F3, 3, 30) (dual of [(6584, 3), 19555, 31]-NRT-code) [i]
9Linear OOA(3197, 4938, F3, 4, 30) (dual of [(4938, 4), 19555, 31]-NRT-code) [i]
10Linear OOA(3197, 3950, F3, 5, 30) (dual of [(3950, 5), 19553, 31]-NRT-code) [i]