Information on Result #2267019
Linear OA(3234, 6570, F3, 44) (dual of [6570, 6336, 45]-code), using 1 times code embedding in larger space based on linear OA(3233, 6569, F3, 44) (dual of [6569, 6336, 45]-code), using
- construction X applied to Ce(43) ⊂ Ce(42) [i] based on
- linear OA(3233, 6561, F3, 44) (dual of [6561, 6328, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3225, 6561, F3, 43) (dual of [6561, 6336, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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 OOA(3234, 3622, F3, 2, 44) (dual of [(3622, 2), 7010, 45]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3234, 3622, F3, 3, 44) (dual of [(3622, 3), 10632, 45]-NRT-code) | [i] | ||
| 3 | Linear OOA(3234, 3622, F3, 4, 44) (dual of [(3622, 4), 14254, 45]-NRT-code) | [i] | ||
| 4 | Linear OOA(3234, 3622, F3, 5, 44) (dual of [(3622, 5), 17876, 45]-NRT-code) | [i] | ||
| 5 | Digital (190, 234, 3622)-net over F3 | [i] | ||
| 6 | Linear OOA(3234, 3285, F3, 2, 44) (dual of [(3285, 2), 6336, 45]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3234, 2190, F3, 3, 44) (dual of [(2190, 3), 6336, 45]-NRT-code) | [i] | ||
| 8 | Linear OOA(3234, 1314, F3, 5, 44) (dual of [(1314, 5), 6336, 45]-NRT-code) | [i] | ||