Information on Result #676214

Linear OA(3134, 2216, F3, 27) (dual of [2216, 2082, 28]-code), using construction XX applied to Ce(27) ⊂ Ce(22) ⊂ Ce(21) based on
  1. linear OA(3127, 2187, F3, 28) (dual of [2187, 2060, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
  2. linear OA(3106, 2187, F3, 23) (dual of [2187, 2081, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  3. linear OA(399, 2187, F3, 22) (dual of [2187, 2088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
  4. linear OA(36, 28, F3, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,3)), using
  5. linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-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 OOA(3134, 1734, F3, 2, 27) (dual of [(1734, 2), 3334, 28]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3134, 1734, F3, 3, 27) (dual of [(1734, 3), 5068, 28]-NRT-code) [i]
3Linear OOA(3134, 1734, F3, 4, 27) (dual of [(1734, 4), 6802, 28]-NRT-code) [i]
4Linear OOA(3134, 1734, F3, 5, 27) (dual of [(1734, 5), 8536, 28]-NRT-code) [i]
5Digital (107, 134, 1734)-net over F3 [i]
6Linear OOA(3134, 1108, F3, 2, 27) (dual of [(1108, 2), 2082, 28]-NRT-code) [i]OOA Folding
7Linear OOA(3134, 554, F3, 4, 27) (dual of [(554, 4), 2082, 28]-NRT-code) [i]
8Linear OOA(3134, 443, F3, 5, 27) (dual of [(443, 5), 2081, 28]-NRT-code) [i]