Information on Result #733262

Linear OA(2767, 784, F27, 26) (dual of [784, 717, 27]-code), using (u, u+v)-construction based on
  1. linear OA(2716, 52, F27, 13) (dual of [52, 36, 14]-code), using
  2. linear OA(2751, 732, F27, 26) (dual of [732, 681, 27]-code), using
    • construction XX applied to C1 = C([727,23]), C2 = C([0,24]), C3 = C1 + C2 = C([0,23]), and C∩ = C1 ∩ C2 = C([727,24]) [i] based on
      1. linear OA(2749, 728, F27, 25) (dual of [728, 679, 26]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,23}, and designed minimum distance d ≥ |I|+1 = 26 [i]
      2. linear OA(2749, 728, F27, 25) (dual of [728, 679, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
      3. 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 = {−1,0,…,24}, and designed minimum distance d ≥ |I|+1 = 27 [i]
      4. linear OA(2747, 728, F27, 24) (dual of [728, 681, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 25 [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(2767, 392, F27, 2, 26) (dual of [(392, 2), 717, 27]-NRT-code) [i]OOA Folding