Information on Result #704130
Linear OA(327, 742, F3, 7) (dual of [742, 715, 8]-code), using construction XX applied to C1 = C([363,367]), C2 = C([361,365]), C3 = C1 + C2 = C([363,365]), and C∩ = C1 ∩ C2 = C([361,367]) based on
- linear OA(319, 728, F3, 5) (dual of [728, 709, 6]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {363,364,365,366,367}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(319, 728, F3, 5) (dual of [728, 709, 6]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {361,362,363,364,365}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(325, 728, F3, 7) (dual of [728, 703, 8]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {361,362,…,367}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(313, 728, F3, 3) (dual of [728, 715, 4]-code or 728-cap in PG(12,3)), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {363,364,365}, and designed minimum distance d ≥ |I|+1 = 4 [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(31, 7, F3, 1) (dual of [7, 6, 2]-code) (see above)
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(327, 390, F3, 2, 7) (dual of [(390, 2), 753, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(327, 390, F3, 3, 7) (dual of [(390, 3), 1143, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(327, 390, F3, 4, 7) (dual of [(390, 4), 1533, 8]-NRT-code) | [i] | ||
| 4 | Linear OOA(327, 390, F3, 5, 7) (dual of [(390, 5), 1923, 8]-NRT-code) | [i] | ||
| 5 | Digital (20, 27, 390)-net over F3 | [i] | ||
| 6 | Linear OOA(327, 371, F3, 2, 7) (dual of [(371, 2), 715, 8]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(327, 247, F3, 3, 7) (dual of [(247, 3), 714, 8]-NRT-code) | [i] | ||
| 8 | Linear OOA(327, 247, F3, 4, 7) (dual of [(247, 4), 961, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 9 | Linear OOA(327, 247, F3, 5, 7) (dual of [(247, 5), 1208, 8]-NRT-code) | [i] | ||
| 10 | Linear OOA(327, 247, F3, 7, 7) (dual of [(247, 7), 1702, 8]-NRT-code) | [i] | ||