Information on Result #731426
Linear OA(998, 1062888, F9, 17) (dual of [1062888, 1062790, 18]-code), using trace code based on linear OA(8149, 531444, F81, 17) (dual of [531444, 531395, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(8149, 531441, F81, 17) (dual of [531441, 531392, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(8146, 531441, F81, 16) (dual of [531441, 531395, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-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(999, 1062889, F9, 17) (dual of [1062889, 1062790, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(998, 1062888, F9, 2, 17) (dual of [(1062888, 2), 2125678, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(998, 1062888, F9, 3, 17) (dual of [(1062888, 3), 3188566, 18]-NRT-code) | [i] | ||
| 4 | Digital (81, 98, 1062888)-net over F9 | [i] | ||
| 5 | Linear OA(999, 1062890, F9, 17) (dual of [1062890, 1062791, 18]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(998, 531444, F9, 2, 17) (dual of [(531444, 2), 1062790, 18]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(998, 354296, F9, 3, 17) (dual of [(354296, 3), 1062790, 18]-NRT-code) | [i] | ||