Information on Result #2267052
Linear OA(3214, 2205, F3, 45) (dual of [2205, 1991, 46]-code), using 2 times code embedding in larger space based on linear OA(3212, 2203, F3, 45) (dual of [2203, 1991, 46]-code), using
- construction X applied to C([0,22]) ⊂ C([0,21]) [i] based on
- linear OA(3211, 2188, F3, 45) (dual of [2188, 1977, 46]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,22], and minimum distance d ≥ |{−22,−21,…,22}|+1 = 46 (BCH-bound) [i]
- linear OA(3197, 2188, F3, 43) (dual of [2188, 1991, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-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 OOA(3214, 1909, F3, 2, 45) (dual of [(1909, 2), 3604, 46]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3214, 1909, F3, 3, 45) (dual of [(1909, 3), 5513, 46]-NRT-code) | [i] | ||
| 3 | Linear OOA(3214, 1909, F3, 4, 45) (dual of [(1909, 4), 7422, 46]-NRT-code) | [i] | ||
| 4 | Linear OOA(3214, 1909, F3, 5, 45) (dual of [(1909, 5), 9331, 46]-NRT-code) | [i] | ||
| 5 | Digital (169, 214, 1909)-net over F3 | [i] | ||
| 6 | Linear OOA(3214, 735, F3, 3, 45) (dual of [(735, 3), 1991, 46]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3214, 441, F3, 5, 45) (dual of [(441, 5), 1991, 46]-NRT-code) | [i] | ||