Information on Result #2265905
Linear OA(3142, 6607, F3, 25) (dual of [6607, 6465, 26]-code), using 2 times code embedding in larger space based on linear OA(3140, 6605, F3, 25) (dual of [6605, 6465, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- 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(397, 6562, F3, 19) (dual of [6562, 6465, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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(3142, 3945, F3, 2, 25) (dual of [(3945, 2), 7748, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3142, 3945, F3, 3, 25) (dual of [(3945, 3), 11693, 26]-NRT-code) | [i] | ||
| 3 | Linear OOA(3142, 3945, F3, 4, 25) (dual of [(3945, 4), 15638, 26]-NRT-code) | [i] | ||
| 4 | Linear OOA(3142, 3945, F3, 5, 25) (dual of [(3945, 5), 19583, 26]-NRT-code) | [i] | ||
| 5 | Digital (117, 142, 3945)-net over F3 | [i] | ||