Information on Result #731587
Linear OA(1668, 131084, F16, 17) (dual of [131084, 131016, 18]-code), using trace code based on linear OA(25634, 65542, F256, 17) (dual of [65542, 65508, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(25629, 65537, F256, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 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 OA(1669, 131085, F16, 17) (dual of [131085, 131016, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1668, 102340, F16, 2, 17) (dual of [(102340, 2), 204612, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (51, 68, 102340)-net over F16 | [i] | ||
| 4 | Linear OOA(1668, 65542, F16, 2, 17) (dual of [(65542, 2), 131016, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1668, 16385, F16, 17, 17) (dual of [(16385, 17), 278477, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |