Information on Result #735720

Linear OA(12867, 2097540, F128, 18) (dual of [2097540, 2097473, 19]-code), using (u, u+v)-construction based on
  1. linear OA(12815, 385, F128, 9) (dual of [385, 370, 10]-code), using
    • construction XX applied to C1 = C([380,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([380,7]) [i] based on
      1. linear OA(12813, 381, F128, 8) (dual of [381, 368, 9]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
      2. linear OA(12813, 381, F128, 8) (dual of [381, 368, 9]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
      3. linear OA(12815, 381, F128, 9) (dual of [381, 366, 10]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
      4. linear OA(12811, 381, F128, 7) (dual of [381, 370, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
      5. linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code) (see above)
  2. linear OA(12852, 2097155, F128, 18) (dual of [2097155, 2097103, 19]-code), using
    • construction X applied to Ce(17) ⊂ Ce(16) [i] based on
      1. linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
      2. linear OA(12849, 2097152, F128, 17) (dual of [2097152, 2097103, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
      3. linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using

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(12867, 1048770, F128, 2, 18) (dual of [(1048770, 2), 2097473, 19]-NRT-code) [i]OOA Folding
2Linear OOA(12867, 699180, F128, 3, 18) (dual of [(699180, 3), 2097473, 19]-NRT-code) [i]