Information on Result #698046
Linear OA(4938, 5764810, F49, 10) (dual of [5764810, 5764772, 11]-code), using construction X applied to Ce(9) ⊂ Ce(7) based on
- linear OA(4937, 5764801, F49, 10) (dual of [5764801, 5764764, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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 OA(4943, 5764860, F49, 10) (dual of [5764860, 5764817, 11]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(4945, 5767163, F49, 10) (dual of [5767163, 5767118, 11]-code) | [i] | ||
| 3 | Linear OOA(4938, 5147608, F49, 2, 10) (dual of [(5147608, 2), 10295178, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4938, 5147608, F49, 3, 10) (dual of [(5147608, 3), 15442786, 11]-NRT-code) | [i] | ||
| 5 | Digital (28, 38, 5147608)-net over F49 | [i] | ||
| 6 | Linear OOA(4938, 2882405, F49, 2, 10) (dual of [(2882405, 2), 5764772, 11]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4938, 1921603, F49, 3, 10) (dual of [(1921603, 3), 5764771, 11]-NRT-code) | [i] | ||
| 8 | Linear OOA(4938, 1152962, F49, 10, 10) (dual of [(1152962, 10), 11529582, 11]-NRT-code) | [i] | OA Folding and Stacking | |