Information on Result #2677767
Linear OOA(3206, 177167, F3, 3, 25) (dual of [(177167, 3), 531295, 26]-NRT-code), using 32 times duplication based on linear OOA(3204, 177167, F3, 3, 25) (dual of [(177167, 3), 531297, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3204, 531501, F3, 25) (dual of [531501, 531297, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3193, 531442, F3, 25) (dual of [531442, 531249, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3145, 531442, F3, 19) (dual of [531442, 531297, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(311, 59, F3, 5) (dual of [59, 48, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
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(3206, 177167, F3, 4, 25) (dual of [(177167, 4), 708462, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3206, 177167, F3, 5, 25) (dual of [(177167, 5), 885629, 26]-NRT-code) | [i] | ||
| 3 | Digital (181, 206, 177167)-net over F3 | [i] | ||