Information on Result #733598

Linear OA(2724, 760, F27, 10) (dual of [760, 736, 11]-code), using (u, u+v)-construction based on
  1. linear OA(275, 28, F27, 5) (dual of [28, 23, 6]-code or 28-arc in PG(4,27)), using
  2. linear OA(2719, 732, F27, 10) (dual of [732, 713, 11]-code), using
    • construction XX applied to C1 = C([727,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([727,8]) [i] based on
      1. linear OA(2717, 728, F27, 9) (dual of [728, 711, 10]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
      2. linear OA(2717, 728, F27, 9) (dual of [728, 711, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
      3. linear OA(2719, 728, F27, 10) (dual of [728, 709, 11]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
      4. linear OA(2715, 728, F27, 8) (dual of [728, 713, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
      5. linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)

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(2724, 380, F27, 2, 10) (dual of [(380, 2), 736, 11]-NRT-code) [i]OOA Folding
2Linear OOA(2724, 152, F27, 10, 10) (dual of [(152, 10), 1496, 11]-NRT-code) [i]OA Folding and Stacking