Information on Result #675514

Linear OA(3223, 6591, F3, 41) (dual of [6591, 6368, 42]-code), using construction X applied to Ce(40) ⊂ Ce(36) based on
  1. linear OA(3217, 6561, F3, 41) (dual of [6561, 6344, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
  2. 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]
  3. linear OA(36, 30, F3, 3) (dual of [30, 24, 4]-code or 30-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(3224, 6592, F3, 41) (dual of [6592, 6368, 42]-code) [i]Code Embedding in Larger Space
2Linear OOA(3223, 3965, F3, 2, 41) (dual of [(3965, 2), 7707, 42]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(3223, 3965, F3, 3, 41) (dual of [(3965, 3), 11672, 42]-NRT-code) [i]
4Linear OOA(3223, 3965, F3, 4, 41) (dual of [(3965, 4), 15637, 42]-NRT-code) [i]
5Linear OOA(3223, 3965, F3, 5, 41) (dual of [(3965, 5), 19602, 42]-NRT-code) [i]
6Digital (182, 223, 3965)-net over F3 [i]
7Linear OOA(3223, 3295, F3, 2, 41) (dual of [(3295, 2), 6367, 42]-NRT-code) [i]OOA Folding
8Linear OOA(3223, 2197, F3, 3, 41) (dual of [(2197, 3), 6368, 42]-NRT-code) [i]
9Linear OOA(3223, 1647, F3, 4, 41) (dual of [(1647, 4), 6365, 42]-NRT-code) [i]
10Linear OOA(3223, 1318, F3, 5, 41) (dual of [(1318, 5), 6367, 42]-NRT-code) [i]