Information on Result #2266665
Linear OA(3175, 2208, F3, 37) (dual of [2208, 2033, 38]-code), using 1 times code embedding in larger space based on linear OA(3174, 2207, F3, 37) (dual of [2207, 2033, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [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(3155, 2188, F3, 33) (dual of [2188, 2033, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(35, 19, F3, 3) (dual of [19, 14, 4]-code or 19-cap in PG(4,3)), 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(3175, 1605, F3, 2, 37) (dual of [(1605, 2), 3035, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3175, 1605, F3, 3, 37) (dual of [(1605, 3), 4640, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(3175, 1605, F3, 4, 37) (dual of [(1605, 4), 6245, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(3175, 1605, F3, 5, 37) (dual of [(1605, 5), 7850, 38]-NRT-code) | [i] | ||
| 5 | Digital (138, 175, 1605)-net over F3 | [i] | ||
| 6 | Linear OOA(3175, 1104, F3, 2, 37) (dual of [(1104, 2), 2033, 38]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3175, 736, F3, 3, 37) (dual of [(736, 3), 2033, 38]-NRT-code) | [i] | ||
| 8 | Linear OOA(3175, 552, F3, 4, 37) (dual of [(552, 4), 2033, 38]-NRT-code) | [i] | ||