Information on Result #676075
Linear OA(3191, 2223, F3, 39) (dual of [2223, 2032, 40]-code), using construction X applied to Ce(39) ⊂ Ce(33) based on
- 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(3155, 2187, F3, 34) (dual of [2187, 2032, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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(3194, 2228, F3, 39) (dual of [2228, 2034, 40]-code) | [i] | Construction X with Varšamov Bound | |
| 2 | Linear OA(3195, 2230, F3, 39) (dual of [2230, 2035, 40]-code) | [i] | ||
| 3 | Linear OA(3196, 2232, F3, 39) (dual of [2232, 2036, 40]-code) | [i] | ||
| 4 | Linear OOA(3191, 1111, F3, 2, 39) (dual of [(1111, 2), 2031, 40]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(3191, 741, F3, 3, 39) (dual of [(741, 3), 2032, 40]-NRT-code) | [i] | ||
| 6 | Linear OOA(3191, 555, F3, 4, 39) (dual of [(555, 4), 2029, 40]-NRT-code) | [i] | ||
| 7 | Linear OOA(3191, 444, F3, 5, 39) (dual of [(444, 5), 2029, 40]-NRT-code) | [i] | ||