Information on Result #812675
Linear OOA(367, 797169, F3, 2, 8) (dual of [(797169, 2), 1594271, 9]-NRT-code), using OOA 2-folding based on linear OA(367, 1594338, F3, 8) (dual of [1594338, 1594271, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(366, 1594323, F3, 8) (dual of [1594323, 1594257, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(353, 1594323, F3, 7) (dual of [1594323, 1594270, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(314, 15, F3, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,3)), using
- dual of repetition code with length 15 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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
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(369, 797170, F3, 2, 8) (dual of [(797170, 2), 1594271, 9]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(368, 797169, F3, 2, 8) (dual of [(797169, 2), 1594270, 9]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3218, 4991470, F3, 2, 16) (dual of [(4991470, 2), 9982722, 17]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 4 | Linear OOA(3233, 4991470, F3, 2, 17) (dual of [(4991470, 2), 9982707, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(367, 797169, F3, 3, 8) (dual of [(797169, 3), 2391440, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(367, 797169, F3, 4, 8) (dual of [(797169, 4), 3188609, 9]-NRT-code) | [i] | ||
| 7 | Linear OOA(367, 797169, F3, 5, 8) (dual of [(797169, 5), 3985778, 9]-NRT-code) | [i] | ||
| 8 | Digital (59, 67, 797169)-net over F3 | [i] | ||