Information on Result #704223
Linear OA(356, 741, F3, 14) (dual of [741, 685, 15]-code), using construction XX applied to C1 = C([352,364]), C2 = C([354,365]), C3 = C1 + C2 = C([354,364]), and C∩ = C1 ∩ C2 = C([352,365]) based on
- linear OA(349, 728, F3, 13) (dual of [728, 679, 14]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {352,353,…,364}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(349, 728, F3, 12) (dual of [728, 679, 13]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {354,355,…,365}, and designed minimum distance d ≥ |I|+1 = 13 [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(343, 728, F3, 11) (dual of [728, 685, 12]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {354,355,…,364}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(31, 7, F3, 1) (dual of [7, 6, 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(356, 396, F3, 2, 14) (dual of [(396, 2), 736, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(356, 396, F3, 3, 14) (dual of [(396, 3), 1132, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(356, 396, F3, 4, 14) (dual of [(396, 4), 1528, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(356, 396, F3, 5, 14) (dual of [(396, 5), 1924, 15]-NRT-code) | [i] | ||
| 5 | Digital (42, 56, 396)-net over F3 | [i] | ||
| 6 | Linear OOA(356, 370, F3, 2, 14) (dual of [(370, 2), 684, 15]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(356, 247, F3, 3, 14) (dual of [(247, 3), 685, 15]-NRT-code) | [i] | ||
| 8 | Linear OOA(356, 185, F3, 4, 14) (dual of [(185, 4), 684, 15]-NRT-code) | [i] | ||