Information on Result #725715

Linear OA(2749, 762, F27, 20) (dual of [762, 713, 21]-code), using construction XX applied to C1 = C([719,7]), C2 = C([0,10]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([719,10]) based on
  1. linear OA(2733, 728, F27, 17) (dual of [728, 695, 18]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−9,−8,…,7}, and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(2721, 728, F27, 11) (dual of [728, 707, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
  3. linear OA(2739, 728, F27, 20) (dual of [728, 689, 21]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−9,−8,…,10}, and designed minimum distance d ≥ |I|+1 = 21 [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(278, 26, F27, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,27)), using
  6. linear OA(272, 8, F27, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,27)), 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(2749, 381, F27, 2, 20) (dual of [(381, 2), 713, 21]-NRT-code) [i]OOA Folding