Information on Result #731569
Linear OA(1652, 131084, F16, 13) (dual of [131084, 131032, 14]-code), using trace code based on linear OA(25626, 65542, F256, 13) (dual of [65542, 65516, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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(1653, 131085, F16, 13) (dual of [131085, 131032, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1652, 125211, F16, 2, 13) (dual of [(125211, 2), 250370, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (39, 52, 125211)-net over F16 | [i] | ||
| 4 | Linear OA(1653, 131086, F16, 13) (dual of [131086, 131033, 14]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(1655, 131090, F16, 13) (dual of [131090, 131035, 14]-code) | [i] | ||
| 6 | Linear OOA(1652, 65542, F16, 2, 13) (dual of [(65542, 2), 131032, 14]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(1652, 21847, F16, 13, 13) (dual of [(21847, 13), 283959, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |