Information on Result #676160

Linear OA(3218, 2216, F3, 45) (dual of [2216, 1998, 46]-code), using construction XX applied to Ce(45) ⊂ Ce(40) ⊂ Ce(39) based on
  1. 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]
  2. linear OA(3190, 2187, F3, 41) (dual of [2187, 1997, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
  3. linear OA(3183, 2187, F3, 40) (dual of [2187, 2004, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [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(3218, 2119, F3, 2, 45) (dual of [(2119, 2), 4020, 46]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3218, 2119, F3, 3, 45) (dual of [(2119, 3), 6139, 46]-NRT-code) [i]
3Linear OOA(3218, 2119, F3, 4, 45) (dual of [(2119, 4), 8258, 46]-NRT-code) [i]
4Linear OOA(3218, 2119, F3, 5, 45) (dual of [(2119, 5), 10377, 46]-NRT-code) [i]
5Digital (173, 218, 2119)-net over F3 [i]
6Linear OOA(3218, 1108, F3, 2, 45) (dual of [(1108, 2), 1998, 46]-NRT-code) [i]OOA Folding
7Linear OOA(3218, 554, F3, 4, 45) (dual of [(554, 4), 1998, 46]-NRT-code) [i]
8Linear OOA(3218, 443, F3, 5, 45) (dual of [(443, 5), 1997, 46]-NRT-code) [i]