Information on Result #876286
Linear OOA(8114, 3283, F81, 2, 7) (dual of [(3283, 2), 6552, 8]-NRT-code), using OOA 2-folding based on linear OA(8114, 6566, F81, 7) (dual of [6566, 6552, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(8114, 6567, F81, 7) (dual of [6567, 6553, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(8113, 6562, F81, 7) (dual of [6562, 6549, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(819, 6562, F81, 5) (dual of [6562, 6553, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
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(8118, 6566, F81, 2, 7) (dual of [(6566, 2), 13114, 8]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8167, 4197584, F81, 2, 14) (dual of [(4197584, 2), 8395101, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(8171, 4197584, F81, 2, 15) (dual of [(4197584, 2), 8395097, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(8114, 3283, F81, 3, 7) (dual of [(3283, 3), 9835, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(8114, 3283, F81, 4, 7) (dual of [(3283, 4), 13118, 8]-NRT-code) | [i] | ||
| 6 | Digital (7, 14, 3283)-net over F81 | [i] | ||