Information on Result #676013

Linear OA(3196, 2214, F3, 41) (dual of [2214, 2018, 42]-code), using construction X applied to Ce(40) ⊂ Ce(36) based on
  1. 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]
  2. 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]
  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(3197, 2215, F3, 41) (dual of [2215, 2018, 42]-code) [i]Code Embedding in Larger Space
2Linear OOA(3196, 1835, F3, 2, 41) (dual of [(1835, 2), 3474, 42]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(3196, 1835, F3, 3, 41) (dual of [(1835, 3), 5309, 42]-NRT-code) [i]
4Linear OOA(3196, 1835, F3, 4, 41) (dual of [(1835, 4), 7144, 42]-NRT-code) [i]
5Linear OOA(3196, 1835, F3, 5, 41) (dual of [(1835, 5), 8979, 42]-NRT-code) [i]
6Digital (155, 196, 1835)-net over F3 [i]
7Linear OOA(3196, 1107, F3, 2, 41) (dual of [(1107, 2), 2018, 42]-NRT-code) [i]OOA Folding
8Linear OOA(3196, 738, F3, 3, 41) (dual of [(738, 3), 2018, 42]-NRT-code) [i]
9Linear OOA(3196, 553, F3, 4, 41) (dual of [(553, 4), 2016, 42]-NRT-code) [i]
10Linear OOA(3196, 442, F3, 5, 41) (dual of [(442, 5), 2014, 42]-NRT-code) [i]