Information on Result #705843

Linear OA(3217, 734, F3, 57) (dual of [734, 517, 58]-code), using construction XX applied to C1 = C([337,392]), C2 = C([336,391]), C3 = C1 + C2 = C([337,391]), and C∩ = C1 ∩ C2 = C([336,392]) based on
  1. linear OA(3214, 728, F3, 56) (dual of [728, 514, 57]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,392}, and designed minimum distance d ≥ |I|+1 = 57 [i]
  2. linear OA(3214, 728, F3, 56) (dual of [728, 514, 57]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,391}, and designed minimum distance d ≥ |I|+1 = 57 [i]
  3. linear OA(3217, 728, F3, 57) (dual of [728, 511, 58]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,392}, and designed minimum distance d ≥ |I|+1 = 58 [i]
  4. linear OA(3211, 728, F3, 55) (dual of [728, 517, 56]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,391}, and designed minimum distance d ≥ |I|+1 = 56 [i]
  5. linear OA(30, 3, F3, 0) (dual of [3, 3, 1]-code), using
  6. linear OA(30, 3, F3, 0) (dual of [3, 3, 1]-code) (see above)

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(3219, 736, F3, 57) (dual of [736, 517, 58]-code) [i]Code Embedding in Larger Space
2Linear OA(3220, 737, F3, 57) (dual of [737, 517, 58]-code) [i]
3Linear OOA(3217, 367, F3, 2, 57) (dual of [(367, 2), 517, 58]-NRT-code) [i]OOA Folding
4Linear OOA(3217, 244, F3, 3, 57) (dual of [(244, 3), 515, 58]-NRT-code) [i]
5Linear OOA(3217, 183, F3, 4, 57) (dual of [(183, 4), 515, 58]-NRT-code) [i]