Information on Result #676023

Linear OA(3162, 2214, F3, 34) (dual of [2214, 2052, 35]-code), using construction X applied to Ce(33) ⊂ Ce(28) based on
  1. linear OA(3155, 2187, F3, 34) (dual of [2187, 2032, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
  2. linear OA(3134, 2187, F3, 29) (dual of [2187, 2053, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(3162, 1579, F3, 2, 34) (dual of [(1579, 2), 2996, 35]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3162, 1579, F3, 3, 34) (dual of [(1579, 3), 4575, 35]-NRT-code) [i]
3Linear OOA(3162, 1579, F3, 4, 34) (dual of [(1579, 4), 6154, 35]-NRT-code) [i]
4Linear OOA(3162, 1579, F3, 5, 34) (dual of [(1579, 5), 7733, 35]-NRT-code) [i]
5Digital (128, 162, 1579)-net over F3 [i]
6Linear OOA(3162, 1107, F3, 2, 34) (dual of [(1107, 2), 2052, 35]-NRT-code) [i]OOA Folding
7Linear OOA(3162, 738, F3, 3, 34) (dual of [(738, 3), 2052, 35]-NRT-code) [i]
8Linear OOA(3162, 553, F3, 4, 34) (dual of [(553, 4), 2050, 35]-NRT-code) [i]
9Linear OOA(3162, 442, F3, 5, 34) (dual of [(442, 5), 2048, 35]-NRT-code) [i]