Information on Result #2266677
Linear OA(3208, 6609, F3, 37) (dual of [6609, 6401, 38]-code), using 4 times code embedding in larger space based on linear OA(3204, 6605, F3, 37) (dual of [6605, 6401, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,15]) [i] based on
- linear OA(3193, 6562, F3, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3161, 6562, F3, 31) (dual of [6562, 6401, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(311, 43, F3, 5) (dual of [43, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 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(3208, 4581, F3, 2, 37) (dual of [(4581, 2), 8954, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3208, 4581, F3, 3, 37) (dual of [(4581, 3), 13535, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(3208, 4581, F3, 4, 37) (dual of [(4581, 4), 18116, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(3208, 4581, F3, 5, 37) (dual of [(4581, 5), 22697, 38]-NRT-code) | [i] | ||
| 5 | Digital (171, 208, 4581)-net over F3 | [i] | ||