Information on Result #731447
Linear OA(9108, 1062904, F9, 18) (dual of [1062904, 1062796, 19]-code), using trace code based on linear OA(8154, 531452, F81, 18) (dual of [531452, 531398, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- linear OA(8152, 531441, F81, 18) (dual of [531441, 531389, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(8143, 531441, F81, 15) (dual of [531441, 531398, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(9109, 1062905, F9, 18) (dual of [1062905, 1062796, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(9108, 1062904, F9, 2, 18) (dual of [(1062904, 2), 2125700, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(9108, 1062904, F9, 3, 18) (dual of [(1062904, 3), 3188604, 19]-NRT-code) | [i] | ||
| 4 | Digital (90, 108, 1062904)-net over F9 | [i] | ||
| 5 | Linear OOA(9108, 531452, F9, 2, 18) (dual of [(531452, 2), 1062796, 19]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(9108, 354301, F9, 3, 18) (dual of [(354301, 3), 1062795, 19]-NRT-code) | [i] | ||
| 7 | Linear OOA(9108, 118100, F9, 18, 18) (dual of [(118100, 18), 2125692, 19]-NRT-code) | [i] | OA Folding and Stacking | |