Information on Result #674752

Linear OA(3128, 177186, F3, 17) (dual of [177186, 177058, 18]-code), using construction X applied to Ce(16) ⊂ Ce(12) based on
  1. linear OA(3122, 177147, F3, 17) (dual of [177147, 177025, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  2. linear OA(389, 177147, F3, 13) (dual of [177147, 177058, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  3. linear OA(36, 39, F3, 3) (dual of [39, 33, 4]-code or 39-cap in PG(5,3)), 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 OA(3129, 177187, F3, 17) (dual of [177187, 177058, 18]-code) [i]Code Embedding in Larger Space
2Linear OA(3130, 177188, F3, 17) (dual of [177188, 177058, 18]-code) [i]
3Linear OA(3131, 177189, F3, 17) (dual of [177189, 177058, 18]-code) [i]
4Linear OA(3132, 177190, F3, 17) (dual of [177190, 177058, 18]-code) [i]
5Linear OA(3132, 177191, F3, 17) (dual of [177191, 177059, 18]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(3128, 88593, F3, 2, 17) (dual of [(88593, 2), 177058, 18]-NRT-code) [i]OOA Folding
7Linear OOA(3128, 59062, F3, 3, 17) (dual of [(59062, 3), 177058, 18]-NRT-code) [i]
8Linear OOA(3128, 44296, F3, 4, 17) (dual of [(44296, 4), 177056, 18]-NRT-code) [i]
9Linear OOA(3128, 35437, F3, 5, 17) (dual of [(35437, 5), 177057, 18]-NRT-code) [i]
10Linear OOA(3128, 22148, F3, 17, 17) (dual of [(22148, 17), 376388, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row