Information on Result #698087
Linear OA(4954, 117673, F49, 17) (dual of [117673, 117619, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,5]) based on
- linear OA(4949, 117650, F49, 17) (dual of [117650, 117601, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(4931, 117650, F49, 11) (dual of [117650, 117619, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(495, 23, F49, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,49)), using
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), using
- Reed–Solomon code RS(44,49) [i]
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), 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, 117673, F49, 2, 17) (dual of [(117673, 2), 235292, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4954, 117673, F49, 3, 17) (dual of [(117673, 3), 352965, 18]-NRT-code) | [i] | ||
| 3 | Digital (37, 54, 117673)-net over F49 | [i] | ||
| 4 | Linear OOA(4954, 58836, F49, 2, 17) (dual of [(58836, 2), 117618, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4954, 39224, F49, 3, 17) (dual of [(39224, 3), 117618, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(4954, 14709, F49, 17, 17) (dual of [(14709, 17), 249999, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |