Information on Result #611571
Linear OA(319, 85, F3, 7) (dual of [85, 66, 8]-code), using construction X applied to C([0,3]) ⊂ C([1,3]) based on
- linear OA(317, 82, F3, 7) (dual of [82, 65, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 82 | 38−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(316, 82, F3, 4) (dual of [82, 66, 5]-code), using the narrow-sense BCH-code C(I) with length 82 | 38−1, defining interval I = [1,3], and minimum distance d ≥ |{1,2,3}| + |{0,39,78,35}∖{39,35}| = 5 (general Roos-bound) [i]
- linear OA(32, 3, F3, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,3)), using
- dual of repetition code with length 3 [i]
- Reed–Solomon code RS(1,3) [i]
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(319, 64, F3, 2, 7) (dual of [(64, 2), 109, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(319, 64, F3, 3, 7) (dual of [(64, 3), 173, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(319, 64, F3, 4, 7) (dual of [(64, 4), 237, 8]-NRT-code) | [i] | ||
| 4 | Linear OOA(319, 64, F3, 5, 7) (dual of [(64, 5), 301, 8]-NRT-code) | [i] | ||
| 5 | Digital (12, 19, 64)-net over F3 | [i] | ||