Information on Result #675851
Linear OA(3121, 2224, F3, 24) (dual of [2224, 2103, 25]-code), using construction X applied to C([0,12]) ⊂ C([0,9]) based on
- linear OA(3113, 2188, F3, 25) (dual of [2188, 2075, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 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(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 OA(3125, 2228, F3, 24) (dual of [2228, 2103, 25]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3126, 2229, F3, 24) (dual of [2229, 2103, 25]-code) | [i] | ||
| 3 | Linear OOA(3121, 1792, F3, 2, 24) (dual of [(1792, 2), 3463, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3121, 1792, F3, 3, 24) (dual of [(1792, 3), 5255, 25]-NRT-code) | [i] | ||
| 5 | Linear OOA(3121, 1792, F3, 4, 24) (dual of [(1792, 4), 7047, 25]-NRT-code) | [i] | ||
| 6 | Linear OOA(3121, 1792, F3, 5, 24) (dual of [(1792, 5), 8839, 25]-NRT-code) | [i] | ||
| 7 | Digital (97, 121, 1792)-net over F3 | [i] | ||
| 8 | Linear OA(3123, 2227, F3, 24) (dual of [2227, 2104, 25]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(3124, 2229, F3, 24) (dual of [2229, 2105, 25]-code) | [i] | ||
| 10 | Linear OA(3125, 2231, F3, 24) (dual of [2231, 2106, 25]-code) | [i] | ||
| 11 | Linear OA(3126, 2233, F3, 24) (dual of [2233, 2107, 25]-code) | [i] | ||
| 12 | Linear OOA(3121, 1112, F3, 2, 24) (dual of [(1112, 2), 2103, 25]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(3121, 741, F3, 3, 24) (dual of [(741, 3), 2102, 25]-NRT-code) | [i] | ||
| 14 | Linear OOA(3121, 556, F3, 4, 24) (dual of [(556, 4), 2103, 25]-NRT-code) | [i] | ||
| 15 | Linear OOA(3121, 444, F3, 5, 24) (dual of [(444, 5), 2099, 25]-NRT-code) | [i] | ||