Information on Result #676010

Linear OA(3204, 2214, F3, 43) (dual of [2214, 2010, 44]-code), using construction X applied to Ce(42) ⊂ Ce(37) based on
  1. linear OA(3197, 2187, F3, 43) (dual of [2187, 1990, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
  2. linear OA(3176, 2187, F3, 38) (dual of [2187, 2011, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
  3. linear OA(37, 27, F3, 4) (dual of [27, 20, 5]-code), using
    • an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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 OOA(3204, 1821, F3, 2, 43) (dual of [(1821, 2), 3438, 44]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3204, 1821, F3, 3, 43) (dual of [(1821, 3), 5259, 44]-NRT-code) [i]
3Linear OOA(3204, 1821, F3, 4, 43) (dual of [(1821, 4), 7080, 44]-NRT-code) [i]
4Linear OOA(3204, 1821, F3, 5, 43) (dual of [(1821, 5), 8901, 44]-NRT-code) [i]
5Digital (161, 204, 1821)-net over F3 [i]
6Linear OOA(3204, 1107, F3, 2, 43) (dual of [(1107, 2), 2010, 44]-NRT-code) [i]OOA Folding
7Linear OOA(3204, 738, F3, 3, 43) (dual of [(738, 3), 2010, 44]-NRT-code) [i]
8Linear OOA(3204, 553, F3, 4, 43) (dual of [(553, 4), 2008, 44]-NRT-code) [i]
9Linear OOA(3204, 442, F3, 5, 43) (dual of [(442, 5), 2006, 44]-NRT-code) [i]