Information on Result #686759
Linear OA(816, 32773, F8, 4) (dual of [32773, 32757, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
- linear OA(816, 32768, F8, 4) (dual of [32768, 32752, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(811, 32768, F8, 3) (dual of [32768, 32757, 4]-code or 32768-cap in PG(10,8)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(80, 5, F8, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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 OA(818, 32782, F8, 4) (dual of [32782, 32764, 5]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(816, 32773, F8, 2, 4) (dual of [(32773, 2), 65530, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(816, 32773, F8, 3, 4) (dual of [(32773, 3), 98303, 5]-NRT-code) | [i] | ||
| 4 | Linear OOA(816, 16386, F8, 2, 4) (dual of [(16386, 2), 32756, 5]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(816, 16386, F8, 3, 4) (dual of [(16386, 3), 49142, 5]-NRT-code) | [i] | OA Folding and Stacking | |