Information on Result #698013
Linear OA(4950, 5764811, F49, 13) (dual of [5764811, 5764761, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,5]) based on
- linear OA(4949, 5764802, F49, 13) (dual of [5764802, 5764753, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(4941, 5764802, F49, 11) (dual of [5764802, 5764761, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(491, 9, F49, 1) (dual of [9, 8, 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
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(4950, 3458021, F49, 2, 13) (dual of [(3458021, 2), 6915992, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4950, 3458021, F49, 3, 13) (dual of [(3458021, 3), 10374013, 14]-NRT-code) | [i] | ||
| 3 | Digital (37, 50, 3458021)-net over F49 | [i] | ||
| 4 | Linear OOA(4950, 2882405, F49, 2, 13) (dual of [(2882405, 2), 5764760, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4950, 1921603, F49, 3, 13) (dual of [(1921603, 3), 5764759, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(4950, 960801, F49, 13, 13) (dual of [(960801, 13), 12490363, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |