Information on Result #2266051
Linear OA(3130, 2205, F3, 27) (dual of [2205, 2075, 28]-code), using 2 times code embedding in larger space based on linear OA(3128, 2203, F3, 27) (dual of [2203, 2075, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- 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(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(31, 15, F3, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(3130, 1451, F3, 2, 27) (dual of [(1451, 2), 2772, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3130, 1451, F3, 3, 27) (dual of [(1451, 3), 4223, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(3130, 1451, F3, 4, 27) (dual of [(1451, 4), 5674, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(3130, 1451, F3, 5, 27) (dual of [(1451, 5), 7125, 28]-NRT-code) | [i] | ||
| 5 | Digital (103, 130, 1451)-net over F3 | [i] | ||
| 6 | Linear OOA(3130, 735, F3, 3, 27) (dual of [(735, 3), 2075, 28]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3130, 441, F3, 5, 27) (dual of [(441, 5), 2075, 28]-NRT-code) | [i] | ||