Information on Result #2267022
Linear OA(3250, 6618, F3, 44) (dual of [6618, 6368, 45]-code), using 2 times code embedding in larger space based on linear OA(3248, 6616, F3, 44) (dual of [6616, 6368, 45]-code), using
- construction X applied to Ce(43) ⊂ Ce(36) [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(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(315, 55, F3, 6) (dual of [55, 40, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-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 OOA(3250, 5524, F3, 2, 44) (dual of [(5524, 2), 10798, 45]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3250, 5524, F3, 3, 44) (dual of [(5524, 3), 16322, 45]-NRT-code) | [i] | ||
| 3 | Linear OOA(3250, 5524, F3, 4, 44) (dual of [(5524, 4), 21846, 45]-NRT-code) | [i] | ||
| 4 | Linear OOA(3250, 5524, F3, 5, 44) (dual of [(5524, 5), 27370, 45]-NRT-code) | [i] | ||
| 5 | Digital (206, 250, 5524)-net over F3 | [i] | ||
| 6 | Linear OOA(3250, 2206, F3, 3, 44) (dual of [(2206, 3), 6368, 45]-NRT-code) | [i] | OOA Folding | |