Information on Result #900416

Linear OOA(2717, 732, F27, 2, 7) (dual of [(732, 2), 1447, 8]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(274, 730, F27, 2, 3) (dual of [(730, 2), 1456, 4]-NRT-code), using
  2. linear OOA(2713, 366, F27, 2, 7) (dual of [(366, 2), 719, 8]-NRT-code), using
    • OOA 2-folding [i] based on linear OA(2713, 732, F27, 7) (dual of [732, 719, 8]-code), using
      • construction XX applied to C1 = C([727,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([727,5]) [i] based on
        1. linear OA(2711, 728, F27, 6) (dual of [728, 717, 7]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
        2. linear OA(2711, 728, F27, 6) (dual of [728, 717, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
        3. linear OA(2713, 728, F27, 7) (dual of [728, 715, 8]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
        4. linear OA(279, 728, F27, 5) (dual of [728, 719, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [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(2783, 4195033, F27, 2, 14) (dual of [(4195033, 2), 8389983, 15]-NRT-code) [i](u, u+v)-Construction for OOAs
2Linear OOA(2788, 4195033, F27, 2, 15) (dual of [(4195033, 2), 8389978, 16]-NRT-code) [i]