Information on Result #676157
Linear OA(3215, 2207, F3, 45) (dual of [2207, 1992, 46]-code), using construction XX applied to Ce(45) ⊂ Ce(42) ⊂ Ce(40) 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(3197, 2187, F3, 43) (dual of [2187, 1990, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3190, 2187, F3, 41) (dual of [2187, 1997, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(31, 17, F3, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [i]
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(3215, 1960, F3, 2, 45) (dual of [(1960, 2), 3705, 46]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3215, 1960, F3, 3, 45) (dual of [(1960, 3), 5665, 46]-NRT-code) | [i] | ||
| 3 | Linear OOA(3215, 1960, F3, 4, 45) (dual of [(1960, 4), 7625, 46]-NRT-code) | [i] | ||
| 4 | Linear OOA(3215, 1960, F3, 5, 45) (dual of [(1960, 5), 9585, 46]-NRT-code) | [i] | ||
| 5 | Digital (170, 215, 1960)-net over F3 | [i] | ||