Information on Result #731654
Linear OA(16108, 131084, F16, 27) (dual of [131084, 130976, 28]-code), using trace code based on linear OA(25654, 65542, F256, 27) (dual of [65542, 65488, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(25649, 65537, F256, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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(16109, 131085, F16, 27) (dual of [131085, 130976, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(16108, 96629, F16, 2, 27) (dual of [(96629, 2), 193150, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (81, 108, 96629)-net over F16 | [i] | ||
| 4 | Linear OOA(16108, 65542, F16, 2, 27) (dual of [(65542, 2), 130976, 28]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(16108, 10083, F16, 27, 27) (dual of [(10083, 27), 272133, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |