Information on Result #733092

Linear OA(27105, 840, F27, 38) (dual of [840, 735, 39]-code), using (u, u+v)-construction based on
  1. linear OA(2733, 108, F27, 19) (dual of [108, 75, 20]-code), using
    • construction XX applied to C1 = C([103,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([103,17]) [i] based on
      1. linear OA(2731, 104, F27, 18) (dual of [104, 73, 19]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(2731, 104, F27, 18) (dual of [104, 73, 19]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
      3. linear OA(2733, 104, F27, 19) (dual of [104, 71, 20]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
      4. linear OA(2729, 104, F27, 17) (dual of [104, 75, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 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(2772, 732, F27, 38) (dual of [732, 660, 39]-code), using
    • construction XX applied to C1 = C([727,35]), C2 = C([0,36]), C3 = C1 + C2 = C([0,35]), and C∩ = C1 ∩ C2 = C([727,36]) [i] based on
      1. linear OA(2770, 728, F27, 37) (dual of [728, 658, 38]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,35}, and designed minimum distance d ≥ |I|+1 = 38 [i]
      2. 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]
      3. 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]
      4. linear OA(2768, 728, F27, 36) (dual of [728, 660, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [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(27105, 420, F27, 2, 38) (dual of [(420, 2), 735, 39]-NRT-code) [i]OOA Folding