Information on Result #699883

Linear OA(12872, 16420, F128, 31) (dual of [16420, 16348, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,9]) based on
  1. linear OA(12861, 16385, F128, 31) (dual of [16385, 16324, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (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(12811, 35, F128, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,128)), 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(6484, 16420, S64, 31) [i]Discarding Parts of the Base for OAs
2Linear OOA(12872, 13240, F128, 2, 31) (dual of [(13240, 2), 26408, 32]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(12872, 13240, F128, 3, 31) (dual of [(13240, 3), 39648, 32]-NRT-code) [i]
4Linear OOA(12872, 13240, F128, 4, 31) (dual of [(13240, 4), 52888, 32]-NRT-code) [i]
5Digital (41, 72, 13240)-net over F128 [i]
6Linear OOA(12872, 8210, F128, 2, 31) (dual of [(8210, 2), 16348, 32]-NRT-code) [i]OOA Folding
7Linear OOA(12872, 5473, F128, 3, 31) (dual of [(5473, 3), 16347, 32]-NRT-code) [i]
8Linear OOA(12872, 4105, F128, 4, 31) (dual of [(4105, 4), 16348, 32]-NRT-code) [i]