Information on Result #631499
Linear OA(361, 112, F3, 23) (dual of [112, 51, 24]-code), using concatenation of two codes based on
- linear OA(2711, 28, F27, 11) (dual of [28, 17, 12]-code or 28-arc in PG(10,27)), using
- extended Reed–Solomon code RSe(17,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(31, 4, F3, 1) (dual of [4, 3, 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.
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 OA(362, 113, F3, 23) (dual of [113, 51, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(363, 114, F3, 23) (dual of [114, 51, 24]-code) | [i] | ||
| 3 | Linear OA(364, 115, F3, 23) (dual of [115, 51, 24]-code) | [i] | ||
| 4 | Linear OA(362, 114, F3, 23) (dual of [114, 52, 24]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(361, 56, F3, 2, 23) (dual of [(56, 2), 51, 24]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(361, 37, F3, 3, 23) (dual of [(37, 3), 50, 24]-NRT-code) | [i] | ||