Information on Result #698313
Linear OA(4954, 2424, F49, 24) (dual of [2424, 2370, 25]-code), using construction X applied to Ce(23) ⊂ Ce(15) based on
- linear OA(4947, 2401, F49, 24) (dual of [2401, 2354, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(497, 23, F49, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,49)), using
- discarding factors / shortening the dual code based on linear OA(497, 49, F49, 7) (dual of [49, 42, 8]-code or 49-arc in PG(6,49)), using
- Reed–Solomon code RS(42,49) [i]
- discarding factors / shortening the dual code based on linear OA(497, 49, F49, 7) (dual of [49, 42, 8]-code or 49-arc in PG(6,49)), 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(4954, 2215, F49, 2, 24) (dual of [(2215, 2), 4376, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4954, 2215, F49, 3, 24) (dual of [(2215, 3), 6591, 25]-NRT-code) | [i] | ||
| 3 | Digital (30, 54, 2215)-net over F49 | [i] | ||
| 4 | Linear OOA(4954, 1212, F49, 2, 24) (dual of [(1212, 2), 2370, 25]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4954, 808, F49, 3, 24) (dual of [(808, 3), 2370, 25]-NRT-code) | [i] | ||