Information on Result #675412
Linear OA(3226, 6570, F3, 43) (dual of [6570, 6344, 44]-code), using construction X applied to Ce(42) ⊂ Ce(40) based on
- 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(3217, 6561, F3, 41) (dual of [6561, 6344, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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
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 OA(3225, 6569, F3, 42) (dual of [6569, 6344, 43]-code) | [i] | Truncation | |
| 2 | Linear OOA(3226, 3313, F3, 2, 43) (dual of [(3313, 2), 6400, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3226, 3313, F3, 3, 43) (dual of [(3313, 3), 9713, 44]-NRT-code) | [i] | ||
| 4 | Linear OOA(3226, 3313, F3, 4, 43) (dual of [(3313, 4), 13026, 44]-NRT-code) | [i] | ||
| 5 | Linear OOA(3226, 3313, F3, 5, 43) (dual of [(3313, 5), 16339, 44]-NRT-code) | [i] | ||
| 6 | Digital (183, 226, 3313)-net over F3 | [i] | ||
| 7 | Linear OOA(3226, 3285, F3, 2, 43) (dual of [(3285, 2), 6344, 44]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3226, 2190, F3, 3, 43) (dual of [(2190, 3), 6344, 44]-NRT-code) | [i] | ||
| 9 | Linear OOA(3226, 1642, F3, 4, 43) (dual of [(1642, 4), 6342, 44]-NRT-code) | [i] | ||
| 10 | Linear OOA(3226, 1314, F3, 5, 43) (dual of [(1314, 5), 6344, 44]-NRT-code) | [i] | ||