Information on Result #704270
Linear OA(388, 764, F3, 20) (dual of [764, 676, 21]-code), using construction XX applied to C1 = C([346,363]), C2 = C([352,365]), C3 = C1 + C2 = C([352,363]), and C∩ = C1 ∩ C2 = C([346,365]) based on
- linear OA(372, 728, F3, 18) (dual of [728, 656, 19]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {346,347,…,363}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(355, 728, F3, 14) (dual of [728, 673, 15]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {352,353,…,365}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(379, 728, F3, 20) (dual of [728, 649, 21]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {346,347,…,365}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(348, 728, F3, 12) (dual of [728, 680, 13]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {352,353,…,363}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(31, 8, F3, 1) (dual of [8, 7, 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(388, 748, F3, 2, 20) (dual of [(748, 2), 1408, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(388, 748, F3, 3, 20) (dual of [(748, 3), 2156, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(388, 748, F3, 4, 20) (dual of [(748, 4), 2904, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(388, 748, F3, 5, 20) (dual of [(748, 5), 3652, 21]-NRT-code) | [i] | ||
| 5 | Digital (68, 88, 748)-net over F3 | [i] | ||
| 6 | Linear OOA(388, 382, F3, 2, 20) (dual of [(382, 2), 676, 21]-NRT-code) | [i] | OOA Folding | |