Information on Result #675519

Linear OA(3200, 6588, F3, 37) (dual of [6588, 6388, 38]-code), using construction X applied to Ce(36) ⊂ Ce(31) based on
  1. linear OA(3193, 6561, F3, 37) (dual of [6561, 6368, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
  2. linear OA(3169, 6561, F3, 32) (dual of [6561, 6392, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [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(3200, 3556, F3, 2, 37) (dual of [(3556, 2), 6912, 38]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3200, 3556, F3, 3, 37) (dual of [(3556, 3), 10468, 38]-NRT-code) [i]
3Linear OOA(3200, 3556, F3, 4, 37) (dual of [(3556, 4), 14024, 38]-NRT-code) [i]
4Linear OOA(3200, 3556, F3, 5, 37) (dual of [(3556, 5), 17580, 38]-NRT-code) [i]
5Digital (163, 200, 3556)-net over F3 [i]
6Linear OOA(3200, 3294, F3, 2, 37) (dual of [(3294, 2), 6388, 38]-NRT-code) [i]OOA Folding
7Linear OOA(3200, 2196, F3, 3, 37) (dual of [(2196, 3), 6388, 38]-NRT-code) [i]
8Linear OOA(3200, 1647, F3, 4, 37) (dual of [(1647, 4), 6388, 38]-NRT-code) [i]
9Linear OOA(3200, 1317, F3, 5, 37) (dual of [(1317, 5), 6385, 38]-NRT-code) [i]