Information on Result #876662
Linear OOA(8156, 265724, F81, 2, 19) (dual of [(265724, 2), 531392, 20]-NRT-code), using OOA 2-folding based on linear OA(8156, 531448, F81, 19) (dual of [531448, 531392, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8156, 531449, F81, 19) (dual of [531449, 531393, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- 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(8149, 531442, F81, 17) (dual of [531442, 531393, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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([0,9]) ⊂ C([0,8]) [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(8167, 265840, F81, 2, 19) (dual of [(265840, 2), 531613, 20]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8156, 234732, F81, 3, 19) (dual of [(234732, 3), 704140, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8156, 234732, F81, 4, 19) (dual of [(234732, 4), 938872, 20]-NRT-code) | [i] | ||
| 4 | Digital (37, 56, 234732)-net over F81 | [i] | ||