Information on Result #2267615
Linear OA(3109, 125, F3, 61) (dual of [125, 16, 62]-code), using 3 times code embedding in larger space based on linear OA(3106, 122, F3, 61) (dual of [122, 16, 62]-code), using
- 1 times truncation [i] based on linear OA(3107, 123, F3, 62) (dual of [123, 16, 63]-code), using
- construction X applied to C([0,60]) ⊂ C([1,60]) [i] based on
- linear OA(3106, 121, F3, 62) (dual of [121, 15, 63]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,60], and minimum distance d ≥ |{−1,0,…,60}|+1 = 63 (BCH-bound) [i]
- linear OA(3105, 121, F3, 60) (dual of [121, 16, 61]-code), using the narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [1,60], and designed minimum distance d ≥ |I|+1 = 61 [i]
- linear OA(31, 2, F3, 1) (dual of [2, 1, 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
- construction X applied to C([0,60]) ⊂ C([1,60]) [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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3109, 25, F3, 5, 61) (dual of [(25, 5), 16, 62]-NRT-code) | [i] | OOA Folding | |