Information on Result #698307
Linear OA(4943, 2421, F49, 19) (dual of [2421, 2378, 20]-code), using construction X applied to Ce(18) ⊂ Ce(11) based on
- linear OA(4937, 2401, F49, 19) (dual of [2401, 2364, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(4923, 2401, F49, 12) (dual of [2401, 2378, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(4943, 2233, F49, 2, 19) (dual of [(2233, 2), 4423, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4943, 2233, F49, 3, 19) (dual of [(2233, 3), 6656, 20]-NRT-code) | [i] | ||
| 3 | Digital (24, 43, 2233)-net over F49 | [i] | ||
| 4 | Linear OOA(4943, 1210, F49, 2, 19) (dual of [(1210, 2), 2377, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4943, 807, F49, 3, 19) (dual of [(807, 3), 2378, 20]-NRT-code) | [i] | ||