Information on Result #733073

Linear OA(27109, 918, F27, 39) (dual of [918, 809, 40]-code), using (u, u+v)-construction based on
  1. linear OA(2735, 186, F27, 19) (dual of [186, 151, 20]-code), using
    • construction XX applied to C1 = C([181,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([181,17]) [i] based on
      1. linear OA(2733, 182, F27, 18) (dual of [182, 149, 19]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(2733, 182, F27, 18) (dual of [182, 149, 19]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
      3. linear OA(2735, 182, F27, 19) (dual of [182, 147, 20]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
      4. linear OA(2731, 182, F27, 17) (dual of [182, 151, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [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(2774, 732, F27, 39) (dual of [732, 658, 40]-code), using
    • construction XX applied to C1 = C([727,36]), C2 = C([0,37]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([727,37]) [i] based on
      1. linear OA(2772, 728, F27, 38) (dual of [728, 656, 39]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,36}, and designed minimum distance d ≥ |I|+1 = 39 [i]
      2. linear OA(2772, 728, F27, 38) (dual of [728, 656, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [i]
      3. linear OA(2774, 728, F27, 39) (dual of [728, 654, 40]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,37}, and designed minimum distance d ≥ |I|+1 = 40 [i]
      4. linear OA(2770, 728, F27, 37) (dual of [728, 658, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
      5. linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
      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(27109, 459, F27, 2, 39) (dual of [(459, 2), 809, 40]-NRT-code) [i]OOA Folding