Information on Result #676209

Linear OA(3129, 2197, F3, 28) (dual of [2197, 2068, 29]-code), using construction XX applied to Ce(27) ⊂ Ce(25) ⊂ Ce(24) based on
  1. linear OA(3127, 2187, F3, 28) (dual of [2187, 2060, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
  2. linear OA(3120, 2187, F3, 26) (dual of [2187, 2067, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
  3. linear OA(3113, 2187, F3, 25) (dual of [2187, 2074, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  4. linear OA(31, 9, F3, 1) (dual of [9, 8, 2]-code), using
  5. linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-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 OOA(3129, 1154, F3, 2, 28) (dual of [(1154, 2), 2179, 29]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3129, 1154, F3, 3, 28) (dual of [(1154, 3), 3333, 29]-NRT-code) [i]
3Linear OOA(3129, 1154, F3, 4, 28) (dual of [(1154, 4), 4487, 29]-NRT-code) [i]
4Linear OOA(3129, 1154, F3, 5, 28) (dual of [(1154, 5), 5641, 29]-NRT-code) [i]
5Digital (101, 129, 1154)-net over F3 [i]
6Linear OOA(3129, 1098, F3, 2, 28) (dual of [(1098, 2), 2067, 29]-NRT-code) [i]OOA Folding
7Linear OOA(3129, 732, F3, 3, 28) (dual of [(732, 3), 2067, 29]-NRT-code) [i]
8Linear OOA(3129, 549, F3, 4, 28) (dual of [(549, 4), 2067, 29]-NRT-code) [i]