Information on Result #674435

Linear OA(3150, 1594368, F3, 17) (dual of [1594368, 1594218, 18]-code), using construction X applied to Ce(16) ⊂ Ce(12) based on
  1. linear OA(3144, 1594323, F3, 17) (dual of [1594323, 1594179, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  2. linear OA(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  3. linear OA(36, 45, F3, 3) (dual of [45, 39, 4]-code or 45-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(3151, 1594369, F3, 17) (dual of [1594369, 1594218, 18]-code) [i]Code Embedding in Larger Space
2Linear OA(3152, 1594370, F3, 17) (dual of [1594370, 1594218, 18]-code) [i]
3Linear OA(3153, 1594371, F3, 17) (dual of [1594371, 1594218, 18]-code) [i]
4Linear OA(3154, 1594372, F3, 17) (dual of [1594372, 1594218, 18]-code) [i]
5Linear OA(3154, 1594373, F3, 17) (dual of [1594373, 1594219, 18]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(3150, 797184, F3, 2, 17) (dual of [(797184, 2), 1594218, 18]-NRT-code) [i]OOA Folding
7Linear OOA(3150, 531456, F3, 3, 17) (dual of [(531456, 3), 1594218, 18]-NRT-code) [i]
8Linear OOA(3150, 398592, F3, 4, 17) (dual of [(398592, 4), 1594218, 18]-NRT-code) [i]
9Linear OOA(3150, 318873, F3, 5, 17) (dual of [(318873, 5), 1594215, 18]-NRT-code) [i]
10Linear OOA(3150, 199295, F3, 17, 17) (dual of [(199295, 17), 3387865, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row