Information on Result #676169

Linear OA(3204, 2216, F3, 42) (dual of [2216, 2012, 43]-code), using construction XX applied to Ce(42) ⊂ Ce(37) ⊂ Ce(36) based on
  1. linear OA(3197, 2187, F3, 43) (dual of [2187, 1990, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
  2. linear OA(3176, 2187, F3, 38) (dual of [2187, 2011, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
  3. linear OA(3169, 2187, F3, 37) (dual of [2187, 2018, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(3204, 2043, F3, 2, 42) (dual of [(2043, 2), 3882, 43]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3204, 2043, F3, 3, 42) (dual of [(2043, 3), 5925, 43]-NRT-code) [i]
3Linear OOA(3204, 2043, F3, 4, 42) (dual of [(2043, 4), 7968, 43]-NRT-code) [i]
4Linear OOA(3204, 2043, F3, 5, 42) (dual of [(2043, 5), 10011, 43]-NRT-code) [i]
5Digital (162, 204, 2043)-net over F3 [i]
6Linear OOA(3204, 1108, F3, 2, 42) (dual of [(1108, 2), 2012, 43]-NRT-code) [i]OOA Folding
7Linear OOA(3204, 554, F3, 4, 42) (dual of [(554, 4), 2012, 43]-NRT-code) [i]
8Linear OOA(3204, 443, F3, 5, 42) (dual of [(443, 5), 2011, 43]-NRT-code) [i]