Information on Result #735645

Linear OA(12859, 16776, F128, 21) (dual of [16776, 16717, 22]-code), using (u, u+v)-construction based on
  1. linear OA(12817, 386, F128, 10) (dual of [386, 369, 11]-code), using
    • construction X applied to Ce(9) ⊂ Ce(7) [i] based on
      1. linear OA(12816, 382, F128, 10) (dual of [382, 366, 11]-code), using an extension Ce(9) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
      2. linear OA(12813, 382, F128, 8) (dual of [382, 369, 9]-code), using an extension Ce(7) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
      3. linear OA(1281, 4, F128, 1) (dual of [4, 3, 2]-code), using
  2. linear OA(12842, 16390, F128, 21) (dual of [16390, 16348, 22]-code), using
    • construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
      1. linear OA(12841, 16385, F128, 21) (dual of [16385, 16344, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
      2. linear OA(12837, 16385, F128, 19) (dual of [16385, 16348, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
      3. linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-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(12859, 8388, F128, 2, 21) (dual of [(8388, 2), 16717, 22]-NRT-code) [i]OOA Folding
2Linear OOA(12859, 5592, F128, 3, 21) (dual of [(5592, 3), 16717, 22]-NRT-code) [i]