Information on Result #705431
Linear OA(3196, 753, F3, 49) (dual of [753, 557, 50]-code), using construction XX applied to C1 = C([725,43]), C2 = C([1,45]), C3 = C1 + C2 = C([1,43]), and C∩ = C1 ∩ C2 = C([725,45]) based on
- linear OA(3184, 728, F3, 47) (dual of [728, 544, 48]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,43}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(3177, 728, F3, 45) (dual of [728, 551, 46]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3190, 728, F3, 49) (dual of [728, 538, 50]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,45}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(3171, 728, F3, 43) (dual of [728, 557, 44]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [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(3196, 376, F3, 2, 49) (dual of [(376, 2), 556, 50]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3196, 251, F3, 3, 49) (dual of [(251, 3), 557, 50]-NRT-code) | [i] | ||
| 3 | Linear OOA(3196, 188, F3, 4, 49) (dual of [(188, 4), 556, 50]-NRT-code) | [i] | ||