Information on Result #675561
Linear OA(3217, 6601, F3, 39) (dual of [6601, 6384, 40]-code), using construction X applied to Ce(39) ⊂ Ce(33) based on
- 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(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(38, 40, F3, 4) (dual of [40, 32, 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
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(3218, 6602, F3, 39) (dual of [6602, 6384, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3217, 3300, F3, 2, 39) (dual of [(3300, 2), 6383, 40]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3217, 2200, F3, 3, 39) (dual of [(2200, 3), 6383, 40]-NRT-code) | [i] | ||
| 4 | Linear OOA(3217, 1650, F3, 4, 39) (dual of [(1650, 4), 6383, 40]-NRT-code) | [i] | ||
| 5 | Linear OOA(3217, 1320, F3, 5, 39) (dual of [(1320, 5), 6383, 40]-NRT-code) | [i] | ||