Information on Result #676158
Linear OA(3217, 2208, F3, 46) (dual of [2208, 1991, 47]-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(34, 19, F3, 2) (dual of [19, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(3217, 1857, F3, 2, 46) (dual of [(1857, 2), 3497, 47]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3217, 1857, F3, 3, 46) (dual of [(1857, 3), 5354, 47]-NRT-code) | [i] | ||
| 3 | Linear OOA(3217, 1857, F3, 4, 46) (dual of [(1857, 4), 7211, 47]-NRT-code) | [i] | ||
| 4 | Linear OOA(3217, 1857, F3, 5, 46) (dual of [(1857, 5), 9068, 47]-NRT-code) | [i] | ||
| 5 | Digital (171, 217, 1857)-net over F3 | [i] | ||
| 6 | Linear OOA(3217, 1104, F3, 2, 46) (dual of [(1104, 2), 1991, 47]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3217, 736, F3, 3, 46) (dual of [(736, 3), 1991, 47]-NRT-code) | [i] | ||
| 8 | Linear OOA(3217, 552, F3, 4, 46) (dual of [(552, 4), 1991, 47]-NRT-code) | [i] | ||