Information on Result #676162

Linear OA(3213, 2219, F3, 44) (dual of [2219, 2006, 45]-code), using construction XX applied to Ce(43) ⊂ Ce(39) ⊂ Ce(37) based on
  1. linear OA(3204, 2187, F3, 44) (dual of [2187, 1983, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
  2. 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]
  3. 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]
  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(3213, 2075, F3, 2, 44) (dual of [(2075, 2), 3937, 45]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3213, 2075, F3, 3, 44) (dual of [(2075, 3), 6012, 45]-NRT-code) [i]
3Linear OOA(3213, 2075, F3, 4, 44) (dual of [(2075, 4), 8087, 45]-NRT-code) [i]
4Linear OOA(3213, 2075, F3, 5, 44) (dual of [(2075, 5), 10162, 45]-NRT-code) [i]
5Digital (169, 213, 2075)-net over F3 [i]
6Linear OOA(3213, 1109, F3, 2, 44) (dual of [(1109, 2), 2005, 45]-NRT-code) [i]OOA Folding