Information on Result #873425
Linear OOA(4944, 58828, F49, 2, 15) (dual of [(58828, 2), 117612, 16]-NRT-code), using OOA 2-folding based on linear OA(4944, 117656, F49, 15) (dual of [117656, 117612, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4944, 117657, F49, 15) (dual of [117657, 117613, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(4943, 117650, F49, 15) (dual of [117650, 117607, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(4937, 117650, F49, 13) (dual of [117650, 117613, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(491, 7, F49, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,7]) ⊂ C([0,6]) [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(4951, 58878, F49, 2, 15) (dual of [(58878, 2), 117705, 16]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(4952, 58879, F49, 2, 15) (dual of [(58879, 2), 117706, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(4954, 58928, F49, 2, 15) (dual of [(58928, 2), 117802, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(4944, 58828, F49, 3, 15) (dual of [(58828, 3), 176440, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (29, 44, 58828)-net over F49 | [i] | ||