Information on Result #698146
Linear OA(4953, 117668, F49, 17) (dual of [117668, 117615, 18]-code), using construction X applied to Ce(16) ⊂ Ce(11) based on
- linear OA(4949, 117649, F49, 17) (dual of [117649, 117600, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(4934, 117649, F49, 12) (dual of [117649, 117615, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(494, 19, F49, 4) (dual of [19, 15, 5]-code or 19-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(4953, 96792, F49, 2, 17) (dual of [(96792, 2), 193531, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4953, 96792, F49, 3, 17) (dual of [(96792, 3), 290323, 18]-NRT-code) | [i] | ||
| 3 | Digital (36, 53, 96792)-net over F49 | [i] | ||
| 4 | Linear OOA(4953, 58834, F49, 2, 17) (dual of [(58834, 2), 117615, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4953, 39222, F49, 3, 17) (dual of [(39222, 3), 117613, 18]-NRT-code) | [i] | ||