Information on Result #676184

Linear OA(3173, 2207, F3, 36) (dual of [2207, 2034, 37]-code), using construction XX applied to Ce(36) ⊂ Ce(33) ⊂ Ce(31) based on
  1. 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]
  2. linear OA(3155, 2187, F3, 34) (dual of [2187, 2032, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
  3. linear OA(3148, 2187, F3, 32) (dual of [2187, 2039, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
  4. linear OA(31, 17, F3, 1) (dual of [17, 16, 2]-code), 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(3173, 1723, F3, 2, 36) (dual of [(1723, 2), 3273, 37]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3173, 1723, F3, 3, 36) (dual of [(1723, 3), 4996, 37]-NRT-code) [i]
3Linear OOA(3173, 1723, F3, 4, 36) (dual of [(1723, 4), 6719, 37]-NRT-code) [i]
4Linear OOA(3173, 1723, F3, 5, 36) (dual of [(1723, 5), 8442, 37]-NRT-code) [i]
5Digital (137, 173, 1723)-net over F3 [i]
6Linear OOA(3173, 1103, F3, 2, 36) (dual of [(1103, 2), 2033, 37]-NRT-code) [i]OOA Folding