Information on Result #686324

Linear OA(8162, 2097194, F8, 26) (dual of [2097194, 2097032, 27]-code), using construction X applied to Ce(25) ⊂ Ce(19) based on
  1. linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
  2. linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
  3. linear OA(87, 42, F8, 5) (dual of [42, 35, 6]-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(8163, 2097195, F8, 26) (dual of [2097195, 2097032, 27]-code) [i]Code Embedding in Larger Space
2Linear OA(8164, 2097196, F8, 26) (dual of [2097196, 2097032, 27]-code) [i]
3Linear OA(8165, 2097197, F8, 26) (dual of [2097197, 2097032, 27]-code) [i]
4Linear OOA(8162, 1601362, F8, 2, 26) (dual of [(1601362, 2), 3202562, 27]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(8162, 1601362, F8, 3, 26) (dual of [(1601362, 3), 4803924, 27]-NRT-code) [i]
6Digital (136, 162, 1601362)-net over F8 [i]
7Linear OA(8164, 2097197, F8, 26) (dual of [2097197, 2097033, 27]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OA(8165, 2097199, F8, 26) (dual of [2097199, 2097034, 27]-code) [i]
9Linear OOA(8162, 1048597, F8, 2, 26) (dual of [(1048597, 2), 2097032, 27]-NRT-code) [i]OOA Folding
10Linear OOA(8162, 699064, F8, 3, 26) (dual of [(699064, 3), 2097030, 27]-NRT-code) [i]