Information on Result #698149
Linear OA(4944, 117668, F49, 14) (dual of [117668, 117624, 15]-code), using construction X applied to Ce(13) ⊂ Ce(8) based on
- linear OA(4940, 117649, F49, 14) (dual of [117649, 117609, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(4925, 117649, F49, 9) (dual of [117649, 117624, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(4944, 117668, F49, 2, 14) (dual of [(117668, 2), 235292, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4944, 117668, F49, 3, 14) (dual of [(117668, 3), 352960, 15]-NRT-code) | [i] | ||
| 3 | Digital (30, 44, 117668)-net over F49 | [i] | ||
| 4 | Linear OOA(4944, 58834, F49, 2, 14) (dual of [(58834, 2), 117624, 15]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4944, 39222, F49, 3, 14) (dual of [(39222, 3), 117622, 15]-NRT-code) | [i] | ||