Information on Result #731418
Linear OA(994, 1062896, F9, 16) (dual of [1062896, 1062802, 17]-code), using trace code based on linear OA(8147, 531448, F81, 16) (dual of [531448, 531401, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- 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(8140, 531441, F81, 14) (dual of [531441, 531401, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(995, 1062897, F9, 16) (dual of [1062897, 1062802, 17]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(994, 1062896, F9, 2, 16) (dual of [(1062896, 2), 2125698, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(994, 1062896, F9, 3, 16) (dual of [(1062896, 3), 3188594, 17]-NRT-code) | [i] | ||
| 4 | Digital (78, 94, 1062896)-net over F9 | [i] | ||
| 5 | Linear OA(995, 1062898, F9, 16) (dual of [1062898, 1062803, 17]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(994, 531448, F9, 2, 16) (dual of [(531448, 2), 1062802, 17]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(994, 354298, F9, 3, 16) (dual of [(354298, 3), 1062800, 17]-NRT-code) | [i] | ||
| 8 | Linear OOA(994, 132862, F9, 16, 16) (dual of [(132862, 16), 2125698, 17]-NRT-code) | [i] | OA Folding and Stacking | |