Information on Result #675615

Linear OA(3241, 6641, F3, 41) (dual of [6641, 6400, 42]-code), using construction X applied to Ce(40) ⊂ Ce(30) 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(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(324, 80, F3, 9) (dual of [80, 56, 10]-code), using
    • the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 10 [i]

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(3242, 6642, F3, 41) (dual of [6642, 6400, 42]-code) [i]Code Embedding in Larger Space
2Linear OOA(3241, 6608, F3, 2, 41) (dual of [(6608, 2), 12975, 42]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(3241, 6608, F3, 3, 41) (dual of [(6608, 3), 19583, 42]-NRT-code) [i]
4Linear OOA(3241, 6608, F3, 4, 41) (dual of [(6608, 4), 26191, 42]-NRT-code) [i]
5Linear OOA(3241, 6608, F3, 5, 41) (dual of [(6608, 5), 32799, 42]-NRT-code) [i]
6Digital (200, 241, 6608)-net over F3 [i]
7Linear OA(3242, 6643, F3, 41) (dual of [6643, 6401, 42]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OOA(3241, 3320, F3, 2, 41) (dual of [(3320, 2), 6399, 42]-NRT-code) [i]OOA Folding
9Linear OOA(3241, 2213, F3, 3, 41) (dual of [(2213, 3), 6398, 42]-NRT-code) [i]
10Linear OOA(3241, 1660, F3, 4, 41) (dual of [(1660, 4), 6399, 42]-NRT-code) [i]
11Linear OOA(3241, 1328, F3, 5, 41) (dual of [(1328, 5), 6399, 42]-NRT-code) [i]