Information on Result #675610
Linear OA(3214, 6630, F3, 37) (dual of [6630, 6416, 38]-code), using construction X applied to Ce(36) ⊂ Ce(27) 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 OA(3215, 6631, F3, 37) (dual of [6631, 6416, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3213, 6629, F3, 36) (dual of [6629, 6416, 37]-code) | [i] | Truncation | |
| 3 | Linear OOA(3214, 5537, F3, 2, 37) (dual of [(5537, 2), 10860, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3214, 5537, F3, 3, 37) (dual of [(5537, 3), 16397, 38]-NRT-code) | [i] | ||
| 5 | Linear OOA(3214, 5537, F3, 4, 37) (dual of [(5537, 4), 21934, 38]-NRT-code) | [i] | ||
| 6 | Linear OOA(3214, 5537, F3, 5, 37) (dual of [(5537, 5), 27471, 38]-NRT-code) | [i] | ||
| 7 | Digital (177, 214, 5537)-net over F3 | [i] | ||
| 8 | Linear OOA(3214, 3315, F3, 2, 37) (dual of [(3315, 2), 6416, 38]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(3214, 2210, F3, 3, 37) (dual of [(2210, 3), 6416, 38]-NRT-code) | [i] | ||
| 10 | Linear OOA(3214, 1657, F3, 4, 37) (dual of [(1657, 4), 6414, 38]-NRT-code) | [i] | ||
| 11 | Linear OOA(3214, 1326, F3, 5, 37) (dual of [(1326, 5), 6416, 38]-NRT-code) | [i] | ||