Information on Result #2266288
Linear OA(3147, 2208, F3, 31) (dual of [2208, 2061, 32]-code), using 1 times code embedding in larger space based on linear OA(3146, 2207, F3, 31) (dual of [2207, 2061, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,13]) [i] based on
- 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(3127, 2188, F3, 27) (dual of [2188, 2061, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (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(3147, 1446, F3, 2, 31) (dual of [(1446, 2), 2745, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3147, 1446, F3, 3, 31) (dual of [(1446, 3), 4191, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(3147, 1446, F3, 4, 31) (dual of [(1446, 4), 5637, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(3147, 1446, F3, 5, 31) (dual of [(1446, 5), 7083, 32]-NRT-code) | [i] | ||
| 5 | Digital (116, 147, 1446)-net over F3 | [i] | ||
| 6 | Linear OOA(3147, 1104, F3, 2, 31) (dual of [(1104, 2), 2061, 32]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3147, 736, F3, 3, 31) (dual of [(736, 3), 2061, 32]-NRT-code) | [i] | ||
| 8 | Linear OOA(3147, 552, F3, 4, 31) (dual of [(552, 4), 2061, 32]-NRT-code) | [i] | ||