Information on Result #1305373
Linear OA(3222, 2289, F3, 45) (dual of [2289, 2067, 46]-code), using 76 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 8 times 0, 1, 12 times 0, 1, 17 times 0, 1, 24 times 0) 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: 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(3222, 2289, F3, 2, 45) (dual of [(2289, 2), 4356, 46]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3222, 2289, F3, 3, 45) (dual of [(2289, 3), 6645, 46]-NRT-code) | [i] | ||
| 3 | Linear OOA(3222, 2289, F3, 4, 45) (dual of [(2289, 4), 8934, 46]-NRT-code) | [i] | ||
| 4 | Linear OOA(3222, 2289, F3, 5, 45) (dual of [(2289, 5), 11223, 46]-NRT-code) | [i] | ||
| 5 | Digital (177, 222, 2289)-net over F3 | [i] | ||