Information on Result #900458

Linear OOA(2748, 4194667, F27, 2, 9) (dual of [(4194667, 2), 8389286, 10]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(277, 366, F27, 2, 4) (dual of [(366, 2), 725, 5]-NRT-code), using
    • OOA 2-folding [i] based on linear OA(277, 732, F27, 4) (dual of [732, 725, 5]-code), using
      • construction XX applied to C1 = C([727,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([727,2]) [i] based on
        1. linear OA(275, 728, F27, 3) (dual of [728, 723, 4]-code or 728-cap in PG(4,27)), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
        2. linear OA(275, 728, F27, 3) (dual of [728, 723, 4]-code or 728-cap in PG(4,27)), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
        3. linear OA(277, 728, F27, 4) (dual of [728, 721, 5]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
        4. linear OA(273, 728, F27, 2) (dual of [728, 725, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [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 OOA(2741, 4194301, F27, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(2748, 2097333, F27, 10, 9) (dual of [(2097333, 10), 20973282, 10]-NRT-code) [i]OOA Folding and Stacking with Additional Row