Information on Result #900521

Linear OOA(2731, 414, F27, 2, 12) (dual of [(414, 2), 797, 13]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(278, 48, F27, 2, 6) (dual of [(48, 2), 88, 7]-NRT-code), using
  2. linear OOA(2723, 366, F27, 2, 12) (dual of [(366, 2), 709, 13]-NRT-code), using
    • OOA 2-folding [i] based on linear OA(2723, 732, F27, 12) (dual of [732, 709, 13]-code), using
      • construction XX applied to C1 = C([727,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([727,10]) [i] based on
        1. linear OA(2721, 728, F27, 11) (dual of [728, 707, 12]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [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(2723, 728, F27, 12) (dual of [728, 705, 13]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
        4. linear OA(2719, 728, F27, 10) (dual of [728, 709, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [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(2731, 137, F27, 14, 12) (dual of [(137, 14), 1887, 13]-NRT-code) [i]OOA Folding and Stacking with Additional Row