Information on Result #952649
Linear OOA(3146, 531446, F3, 3, 17) (dual of [(531446, 3), 1594192, 18]-NRT-code), using OOA 3-folding based on linear OA(3146, 1594338, F3, 17) (dual of [1594338, 1594192, 18]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3144, 1594336, F3, 17) (dual of [1594336, 1594192, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(3144, 1594323, F3, 17) (dual of [1594323, 1594179, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(30, 13, F3, 0) (dual of [13, 13, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
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 OOA(3147, 531446, F3, 3, 17) (dual of [(531446, 3), 1594191, 18]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3146, 501995, F3, 4, 17) (dual of [(501995, 4), 2007834, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3146, 501995, F3, 5, 17) (dual of [(501995, 5), 2509829, 18]-NRT-code) | [i] | ||
| 4 | Digital (129, 146, 501995)-net over F3 | [i] | ||