Information on Result #675740

Linear OA(3222, 3294, F3, 42) (dual of [3294, 3072, 43]-code), using construction X applied to Ce(42) ⊂ Ce(39) based on
  1. linear OA(3221, 3281, F3, 43) (dual of [3281, 3060, 44]-code), using an extension Ce(42) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
  2. linear OA(3209, 3281, F3, 40) (dual of [3281, 3072, 41]-code), using an extension Ce(39) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
  3. linear OA(31, 13, F3, 1) (dual of [13, 12, 2]-code), 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(3223, 3295, F3, 42) (dual of [3295, 3072, 43]-code) [i]Code Embedding in Larger Space
2Linear OOA(3222, 3294, F3, 2, 42) (dual of [(3294, 2), 6366, 43]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(3222, 3294, F3, 3, 42) (dual of [(3294, 3), 9660, 43]-NRT-code) [i]
4Linear OOA(3222, 3294, F3, 4, 42) (dual of [(3294, 4), 12954, 43]-NRT-code) [i]
5Linear OOA(3222, 3294, F3, 5, 42) (dual of [(3294, 5), 16248, 43]-NRT-code) [i]
6Digital (180, 222, 3294)-net over F3 [i]
7Linear OA(3223, 3309, F3, 42) (dual of [3309, 3086, 43]-code) [i]VarÅ¡amov–Edel Lengthening
8Linear OA(3223, 3296, F3, 42) (dual of [3296, 3073, 43]-code) [i]Construction X with VarÅ¡amov Bound
9Linear OOA(3222, 1647, F3, 2, 42) (dual of [(1647, 2), 3072, 43]-NRT-code) [i]OOA Folding
10Linear OOA(3222, 1098, F3, 3, 42) (dual of [(1098, 3), 3072, 43]-NRT-code) [i]
11Linear OOA(3222, 823, F3, 4, 42) (dual of [(823, 4), 3070, 43]-NRT-code) [i]
12Linear OOA(3222, 658, F3, 5, 42) (dual of [(658, 5), 3068, 43]-NRT-code) [i]