Information on Result #731457
Linear OA(9112, 1062898, F9, 19) (dual of [1062898, 1062786, 20]-code), using trace code based on linear OA(8156, 531449, F81, 19) (dual of [531449, 531393, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(8155, 531442, F81, 19) (dual of [531442, 531387, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(8149, 531442, F81, 17) (dual of [531442, 531393, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(811, 7, F81, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 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 OOA(9112, 1062898, F9, 2, 19) (dual of [(1062898, 2), 2125684, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(9112, 1062898, F9, 3, 19) (dual of [(1062898, 3), 3188582, 20]-NRT-code) | [i] | ||
| 3 | Digital (93, 112, 1062898)-net over F9 | [i] | ||
| 4 | Linear OOA(9112, 531449, F9, 2, 19) (dual of [(531449, 2), 1062786, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(9112, 354299, F9, 3, 19) (dual of [(354299, 3), 1062785, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(9112, 118099, F9, 19, 19) (dual of [(118099, 19), 2243769, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |