Information on Result #2266290
Linear OA(3154, 2229, F3, 31) (dual of [2229, 2075, 32]-code), using 3 times code embedding in larger space based on linear OA(3151, 2226, F3, 31) (dual of [2226, 2075, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [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(3113, 2188, F3, 25) (dual of [2188, 2075, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(310, 38, F3, 5) (dual of [38, 28, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(310, 39, F3, 5) (dual of [39, 29, 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(3154, 1893, F3, 2, 31) (dual of [(1893, 2), 3632, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3154, 1893, F3, 3, 31) (dual of [(1893, 3), 5525, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(3154, 1893, F3, 4, 31) (dual of [(1893, 4), 7418, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(3154, 1893, F3, 5, 31) (dual of [(1893, 5), 9311, 32]-NRT-code) | [i] | ||
| 5 | Digital (123, 154, 1893)-net over F3 | [i] | ||