Information on Result #731430
Linear OA(9100, 1062898, F9, 17) (dual of [1062898, 1062798, 18]-code), using trace code based on linear OA(8150, 531449, F81, 17) (dual of [531449, 531399, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- 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(8143, 531442, F81, 15) (dual of [531442, 531399, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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 OA(9101, 1062899, F9, 17) (dual of [1062899, 1062798, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(9100, 1062898, F9, 2, 17) (dual of [(1062898, 2), 2125696, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(9100, 1062898, F9, 3, 17) (dual of [(1062898, 3), 3188594, 18]-NRT-code) | [i] | ||
| 4 | Digital (83, 100, 1062898)-net over F9 | [i] | ||
| 5 | Linear OA(9101, 1062900, F9, 17) (dual of [1062900, 1062799, 18]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(9100, 531449, F9, 2, 17) (dual of [(531449, 2), 1062798, 18]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(9100, 354299, F9, 3, 17) (dual of [(354299, 3), 1062797, 18]-NRT-code) | [i] | ||
| 8 | Linear OOA(9100, 132862, F9, 17, 17) (dual of [(132862, 17), 2258554, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |