Information on Result #731557
Linear OA(1636, 131084, F16, 9) (dual of [131084, 131048, 10]-code), using trace code based on linear OA(25618, 65542, F256, 9) (dual of [65542, 65524, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(25617, 65537, F256, 9) (dual of [65537, 65520, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(25613, 65537, F256, 7) (dual of [65537, 65524, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (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(1637, 131085, F16, 9) (dual of [131085, 131048, 10]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1636, 131084, F16, 2, 9) (dual of [(131084, 2), 262132, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (27, 36, 131084)-net over F16 | [i] | ||
| 4 | Linear OA(1637, 131086, F16, 9) (dual of [131086, 131049, 10]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(1636, 65542, F16, 2, 9) (dual of [(65542, 2), 131048, 10]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(1636, 32770, F16, 9, 9) (dual of [(32770, 9), 294894, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |