Information on Result #733383

Linear OA(2759, 918, F27, 21) (dual of [918, 859, 22]-code), using (u, u+v)-construction based on
  1. linear OA(2718, 186, F27, 10) (dual of [186, 168, 11]-code), using
    • construction XX applied to C1 = C([181,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([181,8]) [i] based on
      1. linear OA(2716, 182, F27, 9) (dual of [182, 166, 10]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
      2. linear OA(2716, 182, F27, 9) (dual of [182, 166, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
      3. linear OA(2718, 182, F27, 10) (dual of [182, 164, 11]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
      4. linear OA(2714, 182, F27, 8) (dual of [182, 168, 9]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [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(2741, 732, F27, 21) (dual of [732, 691, 22]-code), using
    • construction XX applied to C1 = C([727,18]), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([727,19]) [i] based on
      1. linear OA(2739, 728, F27, 20) (dual of [728, 689, 21]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,18}, and designed minimum distance d ≥ |I|+1 = 21 [i]
      2. linear OA(2739, 728, F27, 20) (dual of [728, 689, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
      3. linear OA(2741, 728, F27, 21) (dual of [728, 687, 22]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,19}, and designed minimum distance d ≥ |I|+1 = 22 [i]
      4. linear OA(2737, 728, F27, 19) (dual of [728, 691, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [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(2759, 459, F27, 2, 21) (dual of [(459, 2), 859, 22]-NRT-code) [i]OOA Folding