Information on Result #675400
Linear OA(3105, 6602, F3, 18) (dual of [6602, 6497, 19]-code), using construction X applied to C([0,9]) ⊂ C([0,6]) based on
- linear OA(397, 6562, F3, 19) (dual of [6562, 6465, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(365, 6562, F3, 13) (dual of [6562, 6497, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(38, 40, F3, 4) (dual of [40, 32, 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(3106, 6603, F3, 18) (dual of [6603, 6497, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3105, 4278, F3, 2, 18) (dual of [(4278, 2), 8451, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3105, 4278, F3, 3, 18) (dual of [(4278, 3), 12729, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(3105, 4278, F3, 4, 18) (dual of [(4278, 4), 17007, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(3105, 4278, F3, 5, 18) (dual of [(4278, 5), 21285, 19]-NRT-code) | [i] | ||
| 6 | Digital (87, 105, 4278)-net over F3 | [i] | ||
| 7 | Linear OOA(3105, 3301, F3, 2, 18) (dual of [(3301, 2), 6497, 19]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3105, 2200, F3, 3, 18) (dual of [(2200, 3), 6495, 19]-NRT-code) | [i] | ||
| 9 | Linear OOA(3105, 1650, F3, 4, 18) (dual of [(1650, 4), 6495, 19]-NRT-code) | [i] | ||
| 10 | Linear OOA(3105, 1320, F3, 5, 18) (dual of [(1320, 5), 6495, 19]-NRT-code) | [i] | ||
| 11 | Linear OOA(3105, 733, F3, 18, 18) (dual of [(733, 18), 13089, 19]-NRT-code) | [i] | OA Folding and Stacking | |