Information on Result #873356
Linear OOA(4938, 58828, F49, 2, 13) (dual of [(58828, 2), 117618, 14]-NRT-code), using OOA 2-folding based on linear OA(4938, 117656, F49, 13) (dual of [117656, 117618, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4938, 117657, F49, 13) (dual of [117657, 117619, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- 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(4931, 117650, F49, 11) (dual of [117650, 117619, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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([0,6]) ⊂ C([0,5]) [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(4944, 58878, F49, 2, 13) (dual of [(58878, 2), 117712, 14]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(4945, 58879, F49, 2, 13) (dual of [(58879, 2), 117713, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(4938, 58828, F49, 3, 13) (dual of [(58828, 3), 176446, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (25, 38, 58828)-net over F49 | [i] | ||