Information on Result #686189

Linear OA(8128, 2097168, F8, 21) (dual of [2097168, 2097040, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,9]) based on
  1. linear OA(8127, 2097153, F8, 21) (dual of [2097153, 2097026, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
  2. linear OA(8113, 2097153, F8, 19) (dual of [2097153, 2097040, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
  3. linear OA(81, 15, F8, 1) (dual of [15, 14, 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 OA(8129, 2097169, F8, 21) (dual of [2097169, 2097040, 22]-code) [i]Code Embedding in Larger Space
2Linear OA(8144, 2097233, F8, 21) (dual of [2097233, 2097089, 22]-code) [i](u, u+v)-Construction
3Linear OOA(8128, 1231848, F8, 2, 21) (dual of [(1231848, 2), 2463568, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(8128, 1231848, F8, 3, 21) (dual of [(1231848, 3), 3695416, 22]-NRT-code) [i]
5Digital (107, 128, 1231848)-net over F8 [i]
6Linear OOA(8128, 1048584, F8, 2, 21) (dual of [(1048584, 2), 2097040, 22]-NRT-code) [i]OOA Folding
7Linear OOA(8128, 699056, F8, 3, 21) (dual of [(699056, 3), 2097040, 22]-NRT-code) [i]
8Linear OOA(8128, 209716, F8, 21, 21) (dual of [(209716, 21), 4403908, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row