Information on Result #733214

Linear OA(2782, 839, F27, 30) (dual of [839, 757, 31]-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(2756, 731, F27, 30) (dual of [731, 675, 31]-code), using
    • construction X applied to Ce(29) ⊂ Ce(28) [i] based on
      1. linear OA(2756, 729, F27, 30) (dual of [729, 673, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
      2. linear OA(2754, 729, F27, 29) (dual of [729, 675, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
      3. 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(2782, 419, F27, 2, 30) (dual of [(419, 2), 756, 31]-NRT-code) [i]OOA Folding