Information on Result #699887

Linear OA(12878, 16426, F128, 33) (dual of [16426, 16348, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,9]) based on
  1. linear OA(12865, 16385, F128, 33) (dual of [16385, 16320, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (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(12813, 41, F128, 13) (dual of [41, 28, 14]-code or 41-arc in PG(12,128)), 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
1OA(6491, 16426, S64, 33) [i]Discarding Parts of the Base for OAs
2Linear OOA(12878, 16426, F128, 2, 33) (dual of [(16426, 2), 32774, 34]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(12878, 16426, F128, 3, 33) (dual of [(16426, 3), 49200, 34]-NRT-code) [i]
4Linear OOA(12878, 16426, F128, 4, 33) (dual of [(16426, 4), 65626, 34]-NRT-code) [i]
5Digital (45, 78, 16426)-net over F128 [i]
6Linear OOA(12878, 8213, F128, 2, 33) (dual of [(8213, 2), 16348, 34]-NRT-code) [i]OOA Folding
7Linear OOA(12878, 5475, F128, 3, 33) (dual of [(5475, 3), 16347, 34]-NRT-code) [i]
8Linear OOA(12878, 4106, F128, 4, 33) (dual of [(4106, 4), 16346, 34]-NRT-code) [i]