Information on Result #676171

Linear OA(3199, 2219, F3, 41) (dual of [2219, 2020, 42]-code), using construction XX applied to Ce(40) ⊂ Ce(36) ⊂ Ce(34) 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(3162, 2187, F3, 35) (dual of [2187, 2025, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
  4. linear OA(36, 29, F3, 3) (dual of [29, 23, 4]-code or 29-cap in PG(5,3)), using
  5. linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-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(3199, 1999, F3, 2, 41) (dual of [(1999, 2), 3799, 42]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3199, 1999, F3, 3, 41) (dual of [(1999, 3), 5798, 42]-NRT-code) [i]
3Linear OOA(3199, 1999, F3, 4, 41) (dual of [(1999, 4), 7797, 42]-NRT-code) [i]
4Linear OOA(3199, 1999, F3, 5, 41) (dual of [(1999, 5), 9796, 42]-NRT-code) [i]
5Digital (158, 199, 1999)-net over F3 [i]
6Linear OOA(3199, 1109, F3, 2, 41) (dual of [(1109, 2), 2019, 42]-NRT-code) [i]OOA Folding