Information on Result #691879
Linear OA(1626, 4104, F16, 9) (dual of [4104, 4078, 10]-code), using construction X applied to C([0,4]) ⊂ C([0,3]) based on
- linear OA(1625, 4097, F16, 9) (dual of [4097, 4072, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(1619, 4097, F16, 7) (dual of [4097, 4078, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(161, 7, F16, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(1626, 4104, F16, 2, 9) (dual of [(4104, 2), 8182, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (17, 26, 4104)-net over F16 | [i] | ||
| 3 | Linear OA(1627, 4134, F16, 9) (dual of [4134, 4107, 10]-code) | [i] | Varšamov–Edel Lengthening | |
| 4 | Linear OA(1628, 4481, F16, 9) (dual of [4481, 4453, 10]-code) | [i] | ||
| 5 | Linear OA(1629, 5862, F16, 9) (dual of [5862, 5833, 10]-code) | [i] | ||
| 6 | Linear OOA(1626, 2052, F16, 2, 9) (dual of [(2052, 2), 4078, 10]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(1626, 1025, F16, 9, 9) (dual of [(1025, 9), 9199, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |