Information on Result #698070
Linear OA(4941, 5764825, F49, 10) (dual of [5764825, 5764784, 11]-code), using construction X applied to Ce(9) ⊂ Ce(4) 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(4917, 5764801, F49, 5) (dual of [5764801, 5764784, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(494, 24, F49, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,49)), using
- discarding factors / shortening the dual code based on linear OA(494, 49, F49, 4) (dual of [49, 45, 5]-code or 49-arc in PG(3,49)), using
- Reed–Solomon code RS(45,49) [i]
- discarding factors / shortening the dual code based on linear OA(494, 49, F49, 4) (dual of [49, 45, 5]-code or 49-arc in PG(3,49)), 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(4941, 5764825, F49, 2, 10) (dual of [(5764825, 2), 11529609, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4941, 5764825, F49, 3, 10) (dual of [(5764825, 3), 17294434, 11]-NRT-code) | [i] | ||
| 3 | Digital (31, 41, 5764825)-net over F49 | [i] | ||
| 4 | Linear OOA(4941, 2882412, F49, 2, 10) (dual of [(2882412, 2), 5764783, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4941, 1921608, F49, 3, 10) (dual of [(1921608, 3), 5764783, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(4941, 1152965, F49, 10, 10) (dual of [(1152965, 10), 11529609, 11]-NRT-code) | [i] | OA Folding and Stacking | |