Information on Result #703872
Linear OA(365, 374, F3, 17) (dual of [374, 309, 18]-code), using construction XX applied to C1 = C([167,182]), C2 = C([169,183]), C3 = C1 + C2 = C([169,182]), and C∩ = C1 ∩ C2 = C([167,183]) based on
- linear OA(358, 364, F3, 16) (dual of [364, 306, 17]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {167,168,…,182}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(361, 364, F3, 15) (dual of [364, 303, 16]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {169,170,…,183}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(364, 364, F3, 17) (dual of [364, 300, 18]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {167,168,…,183}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(355, 364, F3, 14) (dual of [364, 309, 15]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {169,170,…,182}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(31, 4, F3, 1) (dual of [4, 3, 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
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-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(365, 336, F3, 2, 17) (dual of [(336, 2), 607, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(365, 336, F3, 3, 17) (dual of [(336, 3), 943, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(365, 336, F3, 4, 17) (dual of [(336, 4), 1279, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(365, 336, F3, 5, 17) (dual of [(336, 5), 1615, 18]-NRT-code) | [i] | ||
| 5 | Digital (48, 65, 336)-net over F3 | [i] | ||
| 6 | Linear OOA(365, 187, F3, 2, 17) (dual of [(187, 2), 309, 18]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(365, 124, F3, 3, 17) (dual of [(124, 3), 307, 18]-NRT-code) | [i] | ||