Information on Result #735688

Linear OA(12852, 16771, F128, 19) (dual of [16771, 16719, 20]-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(12837, 16386, F128, 19) (dual of [16386, 16349, 20]-code), using
    • construction X applied to Ce(18) ⊂ Ce(17) [i] based on
      1. linear OA(12837, 16384, F128, 19) (dual of [16384, 16347, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
      3. linear OA(1280, 2, F128, 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(12852, 8385, F128, 2, 19) (dual of [(8385, 2), 16718, 20]-NRT-code) [i]OOA Folding
2Linear OOA(12852, 5590, F128, 3, 19) (dual of [(5590, 3), 16718, 20]-NRT-code) [i]