Information on Result #2266667
Linear OA(3182, 2229, F3, 37) (dual of [2229, 2047, 38]-code), using 3 times code embedding in larger space based on linear OA(3179, 2226, F3, 37) (dual of [2226, 2047, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,15]) [i] based on
- linear OA(3169, 2188, F3, 37) (dual of [2188, 2019, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3141, 2188, F3, 31) (dual of [2188, 2047, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(310, 38, F3, 5) (dual of [38, 28, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(310, 39, F3, 5) (dual of [39, 29, 6]-code), 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(3182, 2007, F3, 2, 37) (dual of [(2007, 2), 3832, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3182, 2007, F3, 3, 37) (dual of [(2007, 3), 5839, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(3182, 2007, F3, 4, 37) (dual of [(2007, 4), 7846, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(3182, 2007, F3, 5, 37) (dual of [(2007, 5), 9853, 38]-NRT-code) | [i] | ||
| 5 | Digital (145, 182, 2007)-net over F3 | [i] | ||