Information on Result #686206

Linear OA(8131, 2097185, F8, 21) (dual of [2097185, 2097054, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) 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(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
  3. linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), 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(8132, 2097186, F8, 21) (dual of [2097186, 2097054, 22]-code) [i]Code Embedding in Larger Space
2Linear OA(8133, 2097187, F8, 21) (dual of [2097187, 2097054, 22]-code) [i]
3Linear OOA(8131, 1710611, F8, 2, 21) (dual of [(1710611, 2), 3421091, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(8131, 1710611, F8, 3, 21) (dual of [(1710611, 3), 5131702, 22]-NRT-code) [i]
5Digital (110, 131, 1710611)-net over F8 [i]
6Linear OA(8133, 2097188, F8, 21) (dual of [2097188, 2097055, 22]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OOA(8131, 1048592, F8, 2, 21) (dual of [(1048592, 2), 2097053, 22]-NRT-code) [i]OOA Folding
8Linear OOA(8131, 699061, F8, 3, 21) (dual of [(699061, 3), 2097052, 22]-NRT-code) [i]
9Linear OOA(8131, 209718, F8, 21, 21) (dual of [(209718, 21), 4403947, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row