Information on Result #731422
Linear OA(996, 1062904, F9, 16) (dual of [1062904, 1062808, 17]-code), using trace code based on linear OA(8148, 531452, F81, 16) (dual of [531452, 531404, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [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(8137, 531441, F81, 13) (dual of [531441, 531404, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(812, 11, F81, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), 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(997, 1062905, F9, 16) (dual of [1062905, 1062808, 17]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(996, 1062904, F9, 2, 16) (dual of [(1062904, 2), 2125712, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(996, 1062904, F9, 3, 16) (dual of [(1062904, 3), 3188616, 17]-NRT-code) | [i] | ||
| 4 | Digital (80, 96, 1062904)-net over F9 | [i] | ||
| 5 | Linear OOA(996, 531452, F9, 2, 16) (dual of [(531452, 2), 1062808, 17]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(996, 354301, F9, 3, 16) (dual of [(354301, 3), 1062807, 17]-NRT-code) | [i] | ||
| 7 | Linear OOA(996, 132863, F9, 16, 16) (dual of [(132863, 16), 2125712, 17]-NRT-code) | [i] | OA Folding and Stacking | |