Information on Result #2266681
Linear OA(3215, 6631, F3, 37) (dual of [6631, 6416, 38]-code), using 1 times code embedding in larger space based on linear OA(3214, 6630, F3, 37) (dual of [6630, 6416, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(27) [i] based on
- 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(3145, 6561, F3, 28) (dual of [6561, 6416, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(321, 69, F3, 8) (dual of [69, 48, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-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(3215, 5714, F3, 2, 37) (dual of [(5714, 2), 11213, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3215, 5714, F3, 3, 37) (dual of [(5714, 3), 16927, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(3215, 5714, F3, 4, 37) (dual of [(5714, 4), 22641, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(3215, 5714, F3, 5, 37) (dual of [(5714, 5), 28355, 38]-NRT-code) | [i] | ||
| 5 | Digital (178, 215, 5714)-net over F3 | [i] | ||