Information on Result #2266296
Linear OA(3175, 6608, F3, 31) (dual of [6608, 6433, 32]-code), using 3 times code embedding in larger space based on linear OA(3172, 6605, F3, 31) (dual of [6605, 6433, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- 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(3129, 6562, F3, 25) (dual of [6562, 6433, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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(3175, 4227, F3, 2, 31) (dual of [(4227, 2), 8279, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3175, 4227, F3, 3, 31) (dual of [(4227, 3), 12506, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(3175, 4227, F3, 4, 31) (dual of [(4227, 4), 16733, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(3175, 4227, F3, 5, 31) (dual of [(4227, 5), 20960, 32]-NRT-code) | [i] | ||
| 5 | Digital (144, 175, 4227)-net over F3 | [i] | ||
| 6 | Linear OOA(3175, 1652, F3, 4, 31) (dual of [(1652, 4), 6433, 32]-NRT-code) | [i] | OOA Folding | |