Information on Result #698306
Linear OA(4945, 2421, F49, 20) (dual of [2421, 2376, 21]-code), using construction X applied to Ce(19) ⊂ Ce(12) based on
- linear OA(4939, 2401, F49, 20) (dual of [2401, 2362, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(4925, 2401, F49, 13) (dual of [2401, 2376, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(496, 20, F49, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,49)), using
- discarding factors / shortening the dual code based on linear OA(496, 49, F49, 6) (dual of [49, 43, 7]-code or 49-arc in PG(5,49)), using
- Reed–Solomon code RS(43,49) [i]
- discarding factors / shortening the dual code based on linear OA(496, 49, F49, 6) (dual of [49, 43, 7]-code or 49-arc in PG(5,49)), 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, 2122, F49, 2, 20) (dual of [(2122, 2), 4199, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4945, 2122, F49, 3, 20) (dual of [(2122, 3), 6321, 21]-NRT-code) | [i] | ||
| 3 | Digital (25, 45, 2122)-net over F49 | [i] | ||
| 4 | Linear OOA(4945, 1210, F49, 2, 20) (dual of [(1210, 2), 2375, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4945, 807, F49, 3, 20) (dual of [(807, 3), 2376, 21]-NRT-code) | [i] | ||