Information on Result #2267303
Linear OA(3242, 2205, F3, 51) (dual of [2205, 1963, 52]-code), using 2 times code embedding in larger space based on linear OA(3240, 2203, F3, 51) (dual of [2203, 1963, 52]-code), using
- construction X applied to C([0,25]) ⊂ C([0,24]) [i] based on
- linear OA(3239, 2188, F3, 51) (dual of [2188, 1949, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,25], and minimum distance d ≥ |{−25,−24,…,25}|+1 = 52 (BCH-bound) [i]
- linear OA(3225, 2188, F3, 49) (dual of [2188, 1963, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (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(3242, 2078, F3, 2, 51) (dual of [(2078, 2), 3914, 52]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3242, 2078, F3, 3, 51) (dual of [(2078, 3), 5992, 52]-NRT-code) | [i] | ||
| 3 | Linear OOA(3242, 2078, F3, 4, 51) (dual of [(2078, 4), 8070, 52]-NRT-code) | [i] | ||
| 4 | Linear OOA(3242, 2078, F3, 5, 51) (dual of [(2078, 5), 10148, 52]-NRT-code) | [i] | ||
| 5 | Digital (191, 242, 2078)-net over F3 | [i] | ||
| 6 | Linear OOA(3242, 735, F3, 3, 51) (dual of [(735, 3), 1963, 52]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3242, 441, F3, 5, 51) (dual of [(441, 5), 1963, 52]-NRT-code) | [i] | ||