Information on Result #688758

Linear OA(816, 67, F8, 9) (dual of [67, 51, 10]-code), using construction X applied to Ce(8) ⊂ Ce(6) based on
  1. linear OA(815, 64, F8, 9) (dual of [64, 49, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
  2. linear OA(813, 64, F8, 7) (dual of [64, 51, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
  3. linear OA(81, 3, F8, 1) (dual of [3, 2, 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(816, 39, F8, 2, 9) (dual of [(39, 2), 62, 10]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(816, 39, F8, 3, 9) (dual of [(39, 3), 101, 10]-NRT-code) [i]
3Digital (7, 16, 39)-net over F8 [i]
4Linear OA(8164, 2097219, F8, 25) (dual of [2097219, 2097055, 26]-code) [i]Construction X with Extended Narrow-Sense BCH Codes
5Linear OA(8173, 262211, F8, 30) (dual of [262211, 262038, 31]-code) [i]
6Linear OA(8167, 262211, F8, 29) (dual of [262211, 262044, 30]-code) [i]
7Linear OA(8161, 262211, F8, 28) (dual of [262211, 262050, 29]-code) [i]
8Linear OA(8155, 262211, F8, 27) (dual of [262211, 262056, 28]-code) [i]
9Linear OOA(816, 33, F8, 2, 9) (dual of [(33, 2), 50, 10]-NRT-code) [i]OOA Folding
10Linear OOA(816, 22, F8, 3, 9) (dual of [(22, 3), 50, 10]-NRT-code) [i]