Information on Result #2266731
Linear OA(3218, 6618, F3, 38) (dual of [6618, 6400, 39]-code), using 2 times code embedding in larger space based on linear OA(3216, 6616, F3, 38) (dual of [6616, 6400, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(30) [i] based on
- 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(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(3218, 5332, F3, 2, 38) (dual of [(5332, 2), 10446, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3218, 5332, F3, 3, 38) (dual of [(5332, 3), 15778, 39]-NRT-code) | [i] | ||
| 3 | Linear OOA(3218, 5332, F3, 4, 38) (dual of [(5332, 4), 21110, 39]-NRT-code) | [i] | ||
| 4 | Linear OOA(3218, 5332, F3, 5, 38) (dual of [(5332, 5), 26442, 39]-NRT-code) | [i] | ||
| 5 | Digital (180, 218, 5332)-net over F3 | [i] | ||
| 6 | Linear OOA(3218, 2206, F3, 3, 38) (dual of [(2206, 3), 6400, 39]-NRT-code) | [i] | OOA Folding | |