Information on Result #2267100
Linear OA(3223, 2227, F3, 46) (dual of [2227, 2004, 47]-code), using 2 times code embedding in larger space based on linear OA(3221, 2225, F3, 46) (dual of [2225, 2004, 47]-code), using
- construction X applied to Ce(45) ⊂ Ce(39) [i] based on
- linear OA(3211, 2187, F3, 46) (dual of [2187, 1976, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3183, 2187, F3, 40) (dual of [2187, 2004, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(310, 38, F3, 5) (dual of [38, 28, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(310, 39, F3, 5) (dual of [39, 29, 6]-code), 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 OOA(3223, 2163, F3, 2, 46) (dual of [(2163, 2), 4103, 47]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3223, 2163, F3, 3, 46) (dual of [(2163, 3), 6266, 47]-NRT-code) | [i] | ||
| 3 | Linear OOA(3223, 2163, F3, 4, 46) (dual of [(2163, 4), 8429, 47]-NRT-code) | [i] | ||
| 4 | Linear OOA(3223, 2163, F3, 5, 46) (dual of [(2163, 5), 10592, 47]-NRT-code) | [i] | ||
| 5 | Digital (177, 223, 2163)-net over F3 | [i] | ||