Information on Result #876765
Linear OOA(8162, 265724, F81, 2, 21) (dual of [(265724, 2), 531386, 22]-NRT-code), using OOA 2-folding based on linear OA(8162, 531448, F81, 21) (dual of [531448, 531386, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8162, 531449, F81, 21) (dual of [531449, 531387, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(8161, 531442, F81, 21) (dual of [531442, 531381, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(8155, 531442, F81, 19) (dual of [531442, 531387, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(811, 7, F81, 1) (dual of [7, 6, 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([0,10]) ⊂ C([0,9]) [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(8174, 265840, F81, 2, 21) (dual of [(265840, 2), 531606, 22]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8162, 217090, F81, 3, 21) (dual of [(217090, 3), 651208, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8162, 217090, F81, 4, 21) (dual of [(217090, 4), 868298, 22]-NRT-code) | [i] | ||
| 4 | Digital (41, 62, 217090)-net over F81 | [i] | ||