Information on Result #676068
Linear OA(3219, 2223, F3, 45) (dual of [2223, 2004, 46]-code), using construction X applied to Ce(45) ⊂ Ce(39) 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(38, 36, F3, 4) (dual of [36, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-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 OA(3220, 2225, F3, 45) (dual of [2225, 2005, 46]-code) | [i] | Construction X with Varšamov Bound | |
| 2 | Linear OA(3221, 2227, F3, 45) (dual of [2227, 2006, 46]-code) | [i] | ||
| 3 | Linear OA(3222, 2229, F3, 45) (dual of [2229, 2007, 46]-code) | [i] | ||
| 4 | Linear OOA(3219, 1111, F3, 2, 45) (dual of [(1111, 2), 2003, 46]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(3219, 741, F3, 3, 45) (dual of [(741, 3), 2004, 46]-NRT-code) | [i] | ||
| 6 | Linear OOA(3219, 555, F3, 4, 45) (dual of [(555, 4), 2001, 46]-NRT-code) | [i] | ||
| 7 | Linear OOA(3219, 444, F3, 5, 45) (dual of [(444, 5), 2001, 46]-NRT-code) | [i] | ||