Information on Result #704164
Linear OA(355, 753, F3, 13) (dual of [753, 698, 14]-code), using construction XX applied to C1 = C([725,7]), C2 = C([1,9]), C3 = C1 + C2 = C([1,7]), and C∩ = C1 ∩ C2 = C([725,9]) based on
- 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 = {−3,−2,…,7}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(336, 728, F3, 9) (dual of [728, 692, 10]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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 = {−3,−2,…,9}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(330, 728, F3, 7) (dual of [728, 698, 8]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(35, 18, F3, 3) (dual of [18, 13, 4]-code or 18-cap in PG(4,3)), using
- 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
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(355, 530, F3, 2, 13) (dual of [(530, 2), 1005, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(355, 530, F3, 3, 13) (dual of [(530, 3), 1535, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(355, 530, F3, 4, 13) (dual of [(530, 4), 2065, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(355, 530, F3, 5, 13) (dual of [(530, 5), 2595, 14]-NRT-code) | [i] | ||
| 5 | Digital (42, 55, 530)-net over F3 | [i] | ||
| 6 | Linear OOA(355, 376, F3, 2, 13) (dual of [(376, 2), 697, 14]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(355, 251, F3, 3, 13) (dual of [(251, 3), 698, 14]-NRT-code) | [i] | ||
| 8 | Linear OOA(355, 188, F3, 4, 13) (dual of [(188, 4), 697, 14]-NRT-code) | [i] | ||