Information on Result #686804
Linear OA(8164, 32786, F8, 37) (dual of [32786, 32622, 38]-code), using construction X applied to Ce(36) ⊂ Ce(33) based on
- linear OA(8161, 32768, F8, 37) (dual of [32768, 32607, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(83, 18, F8, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(8164, 31893, F8, 2, 37) (dual of [(31893, 2), 63622, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8164, 31893, F8, 3, 37) (dual of [(31893, 3), 95515, 38]-NRT-code) | [i] | ||
| 3 | Digital (127, 164, 31893)-net over F8 | [i] | ||
| 4 | Linear OOA(8164, 16393, F8, 2, 37) (dual of [(16393, 2), 32622, 38]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8164, 10928, F8, 3, 37) (dual of [(10928, 3), 32620, 38]-NRT-code) | [i] | ||