Information on Result #726117

Linear OA(2757, 744, F27, 27) (dual of [744, 687, 28]-code), using construction XX applied to C1 = C([723,20]), C2 = C([0,21]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([723,21]) based on
  1. 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 = {−5,−4,…,20}, and designed minimum distance d ≥ |I|+1 = 27 [i]
  2. linear OA(2743, 728, F27, 22) (dual of [728, 685, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
  3. 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 = {−5,−4,…,21}, and designed minimum distance d ≥ |I|+1 = 28 [i]
  4. linear OA(2741, 728, F27, 21) (dual of [728, 687, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
  5. linear OA(274, 14, F27, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,27)), 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(2757, 618, F27, 2, 27) (dual of [(618, 2), 1179, 28]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (30, 57, 618)-net over F27 [i]
3Linear OOA(2757, 372, F27, 2, 27) (dual of [(372, 2), 687, 28]-NRT-code) [i]OOA Folding