Information on Result #676150
Linear OA(3234, 2218, F3, 49) (dual of [2218, 1984, 50]-code), using construction XX applied to Ce(48) ⊂ Ce(43) ⊂ Ce(42) based on
- linear OA(3225, 2187, F3, 49) (dual of [2187, 1962, 50]-code), using an extension Ce(48) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(3204, 2187, F3, 44) (dual of [2187, 1983, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [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(38, 30, F3, 4) (dual of [30, 22, 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
- 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(3234, 2086, F3, 2, 49) (dual of [(2086, 2), 3938, 50]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3234, 2086, F3, 3, 49) (dual of [(2086, 3), 6024, 50]-NRT-code) | [i] | ||
| 3 | Linear OOA(3234, 2086, F3, 4, 49) (dual of [(2086, 4), 8110, 50]-NRT-code) | [i] | ||
| 4 | Linear OOA(3234, 2086, F3, 5, 49) (dual of [(2086, 5), 10196, 50]-NRT-code) | [i] | ||
| 5 | Digital (185, 234, 2086)-net over F3 | [i] | ||
| 6 | Linear OOA(3234, 1109, F3, 2, 49) (dual of [(1109, 2), 1984, 50]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3234, 739, F3, 3, 49) (dual of [(739, 3), 1983, 50]-NRT-code) | [i] | ||