Information on Result #726422

Linear OA(2776, 753, F27, 36) (dual of [753, 677, 37]-code), using construction XX applied to C1 = C([722,28]), C2 = C([3,29]), C3 = C1 + C2 = C([3,28]), and C∩ = C1 ∩ C2 = C([722,29]) based on
  1. linear OA(2766, 728, F27, 35) (dual of [728, 662, 36]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−6,−5,…,28}, and designed minimum distance d ≥ |I|+1 = 36 [i]
  2. linear OA(2753, 728, F27, 27) (dual of [728, 675, 28]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {3,4,…,29}, and designed minimum distance d ≥ |I|+1 = 28 [i]
  3. linear OA(2768, 728, F27, 36) (dual of [728, 660, 37]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−6,−5,…,29}, and designed minimum distance d ≥ |I|+1 = 37 [i]
  4. linear OA(2751, 728, F27, 26) (dual of [728, 677, 27]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {3,4,…,28}, and designed minimum distance d ≥ |I|+1 = 27 [i]
  5. linear OA(278, 23, F27, 8) (dual of [23, 15, 9]-code or 23-arc in PG(7,27)), using
  6. linear OA(270, 2, F27, 0) (dual of [2, 2, 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(2776, 732, F27, 2, 36) (dual of [(732, 2), 1388, 37]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (40, 76, 732)-net over F27 [i]
3Linear OOA(2776, 376, F27, 2, 36) (dual of [(376, 2), 676, 37]-NRT-code) [i]OOA Folding