Information on Result #675221

Linear OA(3171, 19724, F3, 27) (dual of [19724, 19553, 28]-code), using construction X applied to Ce(27) ⊂ Ce(21) based on
  1. linear OA(3163, 19683, F3, 28) (dual of [19683, 19520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
  2. linear OA(3127, 19683, F3, 22) (dual of [19683, 19556, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
  3. linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
    • the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [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(3171, 9862, F3, 2, 27) (dual of [(9862, 2), 19553, 28]-NRT-code) [i]OOA Folding
2Linear OOA(3171, 6574, F3, 3, 27) (dual of [(6574, 3), 19551, 28]-NRT-code) [i]
3Linear OOA(3171, 4931, F3, 4, 27) (dual of [(4931, 4), 19553, 28]-NRT-code) [i]
4Linear OOA(3171, 3944, F3, 5, 27) (dual of [(3944, 5), 19549, 28]-NRT-code) [i]
5Linear OOA(3171, 1517, F3, 27, 27) (dual of [(1517, 27), 40788, 28]-NRT-code) [i]OOA Folding and Stacking with Additional Row