Information on Result #675620
Linear OA(3250, 6595, F3, 46) (dual of [6595, 6345, 47]-code), using construction XX applied to Ce(45) ⊂ Ce(40) ⊂ Ce(39) based on
- linear OA(3241, 6561, F3, 46) (dual of [6561, 6320, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [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(3209, 6561, F3, 40) (dual of [6561, 6352, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(38, 33, F3, 4) (dual of [33, 25, 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(3250, 4283, F3, 2, 46) (dual of [(4283, 2), 8316, 47]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
2 | Linear OOA(3250, 4283, F3, 3, 46) (dual of [(4283, 3), 12599, 47]-NRT-code) | [i] | ||
3 | Linear OOA(3250, 4283, F3, 4, 46) (dual of [(4283, 4), 16882, 47]-NRT-code) | [i] | ||
4 | Linear OOA(3250, 4283, F3, 5, 46) (dual of [(4283, 5), 21165, 47]-NRT-code) | [i] | ||
5 | Digital (204, 250, 4283)-net over F3 | [i] | ||
6 | Linear OOA(3250, 3297, F3, 2, 46) (dual of [(3297, 2), 6344, 47]-NRT-code) | [i] | OOA Folding | |
7 | Linear OOA(3250, 2198, F3, 3, 46) (dual of [(2198, 3), 6344, 47]-NRT-code) | [i] | ||
8 | Linear OOA(3250, 1319, F3, 5, 46) (dual of [(1319, 5), 6345, 47]-NRT-code) | [i] |