Information on Result #698282
Linear OA(4945, 2415, F49, 21) (dual of [2415, 2370, 22]-code), using construction X applied to Ce(20) ⊂ Ce(15) based on
- linear OA(4941, 2401, F49, 21) (dual of [2401, 2360, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4931, 2401, F49, 16) (dual of [2401, 2370, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(494, 14, F49, 4) (dual of [14, 10, 5]-code or 14-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(4945, 1347, F49, 2, 21) (dual of [(1347, 2), 2649, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4945, 1347, F49, 3, 21) (dual of [(1347, 3), 3996, 22]-NRT-code) | [i] | ||
| 3 | Digital (24, 45, 1347)-net over F49 | [i] | ||
| 4 | Linear OOA(4945, 1207, F49, 2, 21) (dual of [(1207, 2), 2369, 22]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4945, 805, F49, 3, 21) (dual of [(805, 3), 2370, 22]-NRT-code) | [i] | ||