Information on Result #731692
Linear OA(16124, 131084, F16, 31) (dual of [131084, 130960, 32]-code), using trace code based on linear OA(25662, 65542, F256, 31) (dual of [65542, 65480, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,14]) [i] based on
- linear OA(25661, 65537, F256, 31) (dual of [65537, 65476, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(25657, 65537, F256, 29) (dual of [65537, 65480, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (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(16125, 131085, F16, 31) (dual of [131085, 130960, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(16124, 99562, F16, 2, 31) (dual of [(99562, 2), 199000, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (93, 124, 99562)-net over F16 | [i] | ||
| 4 | Linear OOA(16124, 65542, F16, 2, 31) (dual of [(65542, 2), 130960, 32]-NRT-code) | [i] | OOA Folding | |