Information on Result #676000

Linear OA(3238, 2214, F3, 50) (dual of [2214, 1976, 51]-code), using construction X applied to Ce(49) ⊂ Ce(45) based on
  1. linear OA(3232, 2187, F3, 50) (dual of [2187, 1955, 51]-code), using an extension Ce(49) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
  2. linear OA(3211, 2187, F3, 46) (dual of [2187, 1976, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
  3. linear OA(36, 27, F3, 3) (dual of [27, 21, 4]-code or 27-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(3239, 2215, F3, 50) (dual of [2215, 1976, 51]-code) [i]Code Embedding in Larger Space
2Linear OOA(3238, 2081, F3, 2, 50) (dual of [(2081, 2), 3924, 51]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(3238, 2081, F3, 3, 50) (dual of [(2081, 3), 6005, 51]-NRT-code) [i]
4Linear OOA(3238, 2081, F3, 4, 50) (dual of [(2081, 4), 8086, 51]-NRT-code) [i]
5Linear OOA(3238, 2081, F3, 5, 50) (dual of [(2081, 5), 10167, 51]-NRT-code) [i]
6Digital (188, 238, 2081)-net over F3 [i]
7Linear OOA(3238, 1107, F3, 2, 50) (dual of [(1107, 2), 1976, 51]-NRT-code) [i]OOA Folding
8Linear OOA(3238, 738, F3, 3, 50) (dual of [(738, 3), 1976, 51]-NRT-code) [i]
9Linear OOA(3238, 553, F3, 4, 50) (dual of [(553, 4), 1974, 51]-NRT-code) [i]
10Linear OOA(3238, 442, F3, 5, 50) (dual of [(442, 5), 1972, 51]-NRT-code) [i]