Information on Result #698089
Linear OA(4942, 117673, F49, 13) (dual of [117673, 117631, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,3]) based on
- linear OA(4937, 117650, F49, 13) (dual of [117650, 117613, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(4919, 117650, F49, 7) (dual of [117650, 117631, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (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(4942, 117673, F49, 2, 13) (dual of [(117673, 2), 235304, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4942, 117673, F49, 3, 13) (dual of [(117673, 3), 352977, 14]-NRT-code) | [i] | ||
| 3 | Digital (29, 42, 117673)-net over F49 | [i] | ||
| 4 | Linear OOA(4942, 58836, F49, 2, 13) (dual of [(58836, 2), 117630, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4942, 39224, F49, 3, 13) (dual of [(39224, 3), 117630, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(4942, 19612, F49, 13, 13) (dual of [(19612, 13), 254914, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |