Information on Result #676005

Linear OA(3218, 2214, F3, 46) (dual of [2214, 1996, 47]-code), using construction X applied to Ce(45) ⊂ Ce(40) 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(37, 27, F3, 4) (dual of [27, 20, 5]-code), using
    • an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]

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, 1905, F3, 2, 46) (dual of [(1905, 2), 3592, 47]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3218, 1905, F3, 3, 46) (dual of [(1905, 3), 5497, 47]-NRT-code) [i]
3Linear OOA(3218, 1905, F3, 4, 46) (dual of [(1905, 4), 7402, 47]-NRT-code) [i]
4Linear OOA(3218, 1905, F3, 5, 46) (dual of [(1905, 5), 9307, 47]-NRT-code) [i]
5Digital (172, 218, 1905)-net over F3 [i]
6Linear OOA(3218, 1107, F3, 2, 46) (dual of [(1107, 2), 1996, 47]-NRT-code) [i]OOA Folding
7Linear OOA(3218, 738, F3, 3, 46) (dual of [(738, 3), 1996, 47]-NRT-code) [i]
8Linear OOA(3218, 553, F3, 4, 46) (dual of [(553, 4), 1994, 47]-NRT-code) [i]
9Linear OOA(3218, 442, F3, 5, 46) (dual of [(442, 5), 1992, 47]-NRT-code) [i]