Information on Result #675522

Linear OA(3191, 6591, F3, 35) (dual of [6591, 6400, 36]-code), using construction X applied to Ce(34) ⊂ Ce(30) based on
  1. linear OA(3185, 6561, F3, 35) (dual of [6561, 6376, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
  2. linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(3192, 6592, F3, 35) (dual of [6592, 6400, 36]-code) [i]Code Embedding in Larger Space
2Linear OOA(3191, 3645, F3, 2, 35) (dual of [(3645, 2), 7099, 36]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(3191, 3645, F3, 3, 35) (dual of [(3645, 3), 10744, 36]-NRT-code) [i]
4Linear OOA(3191, 3645, F3, 4, 35) (dual of [(3645, 4), 14389, 36]-NRT-code) [i]
5Linear OOA(3191, 3645, F3, 5, 35) (dual of [(3645, 5), 18034, 36]-NRT-code) [i]
6Digital (156, 191, 3645)-net over F3 [i]
7Linear OOA(3191, 3295, F3, 2, 35) (dual of [(3295, 2), 6399, 36]-NRT-code) [i]OOA Folding
8Linear OOA(3191, 2197, F3, 3, 35) (dual of [(2197, 3), 6400, 36]-NRT-code) [i]
9Linear OOA(3191, 1647, F3, 4, 35) (dual of [(1647, 4), 6397, 36]-NRT-code) [i]
10Linear OOA(3191, 1318, F3, 5, 35) (dual of [(1318, 5), 6399, 36]-NRT-code) [i]