Information on Result #675667
Linear OA(3166, 6585, F3, 30) (dual of [6585, 6419, 31]-code), using construction XX applied to Ce(30) ⊂ Ce(27) ⊂ Ce(25) based on
- 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(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(3137, 6561, F3, 26) (dual of [6561, 6424, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(31, 20, F3, 1) (dual of [20, 19, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 4, F3, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
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(3166, 3634, F3, 2, 30) (dual of [(3634, 2), 7102, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3166, 3634, F3, 3, 30) (dual of [(3634, 3), 10736, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(3166, 3634, F3, 4, 30) (dual of [(3634, 4), 14370, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(3166, 3634, F3, 5, 30) (dual of [(3634, 5), 18004, 31]-NRT-code) | [i] | ||
| 5 | Digital (136, 166, 3634)-net over F3 | [i] | ||
| 6 | Linear OOA(3166, 3292, F3, 2, 30) (dual of [(3292, 2), 6418, 31]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3166, 2195, F3, 3, 30) (dual of [(2195, 3), 6419, 31]-NRT-code) | [i] | ||
| 8 | Linear OOA(3166, 1646, F3, 4, 30) (dual of [(1646, 4), 6418, 31]-NRT-code) | [i] | ||
| 9 | Linear OOA(3166, 1317, F3, 5, 30) (dual of [(1317, 5), 6419, 31]-NRT-code) | [i] | ||