Information on Result #675754
Linear OA(3212, 2203, F3, 45) (dual of [2203, 1991, 46]-code), using construction X applied to C([0,22]) ⊂ C([0,21]) 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 OA(3213, 2204, F3, 45) (dual of [2204, 1991, 46]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3214, 2205, F3, 45) (dual of [2205, 1991, 46]-code) | [i] | ||
| 3 | Linear OOA(3212, 1812, F3, 2, 45) (dual of [(1812, 2), 3412, 46]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3212, 1812, F3, 3, 45) (dual of [(1812, 3), 5224, 46]-NRT-code) | [i] | ||
| 5 | Linear OOA(3212, 1812, F3, 4, 45) (dual of [(1812, 4), 7036, 46]-NRT-code) | [i] | ||
| 6 | Linear OOA(3212, 1812, F3, 5, 45) (dual of [(1812, 5), 8848, 46]-NRT-code) | [i] | ||
| 7 | Digital (167, 212, 1812)-net over F3 | [i] | ||
| 8 | Linear OA(3216, 2210, F3, 45) (dual of [2210, 1994, 46]-code) | [i] | Varšamov–Edel Lengthening | |
| 9 | Linear OA(3218, 2220, F3, 45) (dual of [2220, 2002, 46]-code) | [i] | ||
| 10 | Linear OA(3219, 2230, F3, 45) (dual of [2230, 2011, 46]-code) | [i] | ||
| 11 | Linear OA(3220, 2244, F3, 45) (dual of [2244, 2024, 46]-code) | [i] | ||
| 12 | Linear OA(3221, 2263, F3, 45) (dual of [2263, 2042, 46]-code) | [i] | ||
| 13 | Linear OA(3222, 2289, F3, 45) (dual of [2289, 2067, 46]-code) | [i] | ||
| 14 | Linear OA(3223, 2322, F3, 45) (dual of [2322, 2099, 46]-code) | [i] | ||
| 15 | Linear OA(3224, 2363, F3, 45) (dual of [2363, 2139, 46]-code) | [i] | ||
| 16 | Linear OA(3225, 2411, F3, 45) (dual of [2411, 2186, 46]-code) | [i] | ||
| 17 | Linear OOA(3212, 1101, F3, 2, 45) (dual of [(1101, 2), 1990, 46]-NRT-code) | [i] | OOA Folding | |
| 18 | Linear OOA(3212, 734, F3, 3, 45) (dual of [(734, 3), 1990, 46]-NRT-code) | [i] | ||
| 19 | Linear OOA(3212, 550, F3, 4, 45) (dual of [(550, 4), 1988, 46]-NRT-code) | [i] | ||
| 20 | Linear OOA(3212, 440, F3, 5, 45) (dual of [(440, 5), 1988, 46]-NRT-code) | [i] | ||