Information on Result #704276
Linear OA(379, 753, F3, 19) (dual of [753, 674, 20]-code), using construction XX applied to C1 = C([725,13]), C2 = C([1,15]), C3 = C1 + C2 = C([1,13]), and C∩ = C1 ∩ C2 = C([725,15]) based on
- linear OA(367, 728, F3, 17) (dual of [728, 661, 18]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,13}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(360, 728, F3, 15) (dual of [728, 668, 16]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(373, 728, F3, 19) (dual of [728, 655, 20]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,15}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(354, 728, F3, 13) (dual of [728, 674, 14]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(379, 540, F3, 2, 19) (dual of [(540, 2), 1001, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(379, 540, F3, 3, 19) (dual of [(540, 3), 1541, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(379, 540, F3, 4, 19) (dual of [(540, 4), 2081, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(379, 540, F3, 5, 19) (dual of [(540, 5), 2621, 20]-NRT-code) | [i] | ||
| 5 | Digital (60, 79, 540)-net over F3 | [i] | ||
| 6 | Linear OOA(379, 376, F3, 2, 19) (dual of [(376, 2), 673, 20]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(379, 251, F3, 3, 19) (dual of [(251, 3), 674, 20]-NRT-code) | [i] | ||
| 8 | Linear OOA(379, 188, F3, 4, 19) (dual of [(188, 4), 673, 20]-NRT-code) | [i] | ||