Information on Result #675630
Linear OA(3234, 6595, F3, 43) (dual of [6595, 6361, 44]-code), using construction XX applied to Ce(42) ⊂ Ce(37) ⊂ Ce(36) 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(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3193, 6561, F3, 37) (dual of [6561, 6368, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(3234, 4114, F3, 2, 43) (dual of [(4114, 2), 7994, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3234, 4114, F3, 3, 43) (dual of [(4114, 3), 12108, 44]-NRT-code) | [i] | ||
| 3 | Linear OOA(3234, 4114, F3, 4, 43) (dual of [(4114, 4), 16222, 44]-NRT-code) | [i] | ||
| 4 | Linear OOA(3234, 4114, F3, 5, 43) (dual of [(4114, 5), 20336, 44]-NRT-code) | [i] | ||
| 5 | Digital (191, 234, 4114)-net over F3 | [i] | ||
| 6 | Linear OOA(3234, 3297, F3, 2, 43) (dual of [(3297, 2), 6360, 44]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3234, 2198, F3, 3, 43) (dual of [(2198, 3), 6360, 44]-NRT-code) | [i] | ||
| 8 | Linear OOA(3234, 1319, F3, 5, 43) (dual of [(1319, 5), 6361, 44]-NRT-code) | [i] | ||