Information on Result #675860
Linear OA(393, 2224, F3, 18) (dual of [2224, 2131, 19]-code), using construction X applied to C([0,9]) ⊂ C([0,6]) based on
- linear OA(385, 2188, F3, 19) (dual of [2188, 2103, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(357, 2188, F3, 13) (dual of [2188, 2131, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(38, 36, F3, 4) (dual of [36, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-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(393, 1869, F3, 2, 18) (dual of [(1869, 2), 3645, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(393, 1869, F3, 3, 18) (dual of [(1869, 3), 5514, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(393, 1869, F3, 4, 18) (dual of [(1869, 4), 7383, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(393, 1869, F3, 5, 18) (dual of [(1869, 5), 9252, 19]-NRT-code) | [i] | ||
| 5 | Digital (75, 93, 1869)-net over F3 | [i] | ||
| 6 | Linear OA(395, 2227, F3, 18) (dual of [2227, 2132, 19]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(393, 1112, F3, 2, 18) (dual of [(1112, 2), 2131, 19]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(393, 741, F3, 3, 18) (dual of [(741, 3), 2130, 19]-NRT-code) | [i] | ||
| 9 | Linear OOA(393, 556, F3, 4, 18) (dual of [(556, 4), 2131, 19]-NRT-code) | [i] | ||
| 10 | Linear OOA(393, 444, F3, 5, 18) (dual of [(444, 5), 2127, 19]-NRT-code) | [i] | ||