Information on Result #698041
Linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(499, 5764801, F49, 3) (dual of [5764801, 5764792, 4]-code or 5764801-cap in PG(8,49)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-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(4915, 5764855, F49, 4) (dual of [5764855, 5764840, 5]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(4913, 5764805, F49, 2, 4) (dual of [(5764805, 2), 11529597, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4913, 5764805, F49, 3, 4) (dual of [(5764805, 3), 17294402, 5]-NRT-code) | [i] | ||
| 4 | Linear OOA(4913, 2882402, F49, 2, 4) (dual of [(2882402, 2), 5764791, 5]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4913, 2882402, F49, 3, 4) (dual of [(2882402, 3), 8647193, 5]-NRT-code) | [i] | OA Folding and Stacking | |