Information on Result #733198

Linear OA(2784, 840, F27, 31) (dual of [840, 756, 32]-code), using (u, u+v)-construction based on
  1. linear OA(2726, 108, F27, 15) (dual of [108, 82, 16]-code), using
    • construction XX applied to C1 = C([103,12]), C2 = C([0,13]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([103,13]) [i] based on
      1. linear OA(2724, 104, F27, 14) (dual of [104, 80, 15]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
      2. linear OA(2724, 104, F27, 14) (dual of [104, 80, 15]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
      3. linear OA(2726, 104, F27, 15) (dual of [104, 78, 16]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
      4. linear OA(2722, 104, F27, 13) (dual of [104, 82, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [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)
  2. linear OA(2758, 732, F27, 31) (dual of [732, 674, 32]-code), using
    • construction XX applied to C1 = C([727,28]), C2 = C([0,29]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([727,29]) [i] based on
      1. linear OA(2756, 728, F27, 30) (dual of [728, 672, 31]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,28}, and designed minimum distance d ≥ |I|+1 = 31 [i]
      2. linear OA(2756, 728, F27, 30) (dual of [728, 672, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
      3. linear OA(2758, 728, F27, 31) (dual of [728, 670, 32]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,29}, and designed minimum distance d ≥ |I|+1 = 32 [i]
      4. linear OA(2754, 728, F27, 29) (dual of [728, 674, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
      5. linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
      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(2784, 420, F27, 2, 31) (dual of [(420, 2), 756, 32]-NRT-code) [i]OOA Folding