Information on Result #676164
Linear OA(3199, 2197, F3, 43) (dual of [2197, 1998, 44]-code), using construction XX applied to Ce(42) ⊂ Ce(40) ⊂ Ce(39) based on
- 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(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(31, 9, F3, 1) (dual of [9, 8, 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(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(3199, 1588, F3, 2, 43) (dual of [(1588, 2), 2977, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3199, 1588, F3, 3, 43) (dual of [(1588, 3), 4565, 44]-NRT-code) | [i] | ||
| 3 | Linear OOA(3199, 1588, F3, 4, 43) (dual of [(1588, 4), 6153, 44]-NRT-code) | [i] | ||
| 4 | Linear OOA(3199, 1588, F3, 5, 43) (dual of [(1588, 5), 7741, 44]-NRT-code) | [i] | ||
| 5 | Digital (156, 199, 1588)-net over F3 | [i] | ||
| 6 | Linear OOA(3199, 1098, F3, 2, 43) (dual of [(1098, 2), 1997, 44]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3199, 732, F3, 3, 43) (dual of [(732, 3), 1997, 44]-NRT-code) | [i] | ||
| 8 | Linear OOA(3199, 549, F3, 4, 43) (dual of [(549, 4), 1997, 44]-NRT-code) | [i] | ||