Information on Result #705498
Linear OA(3201, 752, F3, 50) (dual of [752, 551, 51]-code), using construction XX applied to C1 = C([725,45]), C2 = C([1,46]), C3 = C1 + C2 = C([1,45]), and C∩ = C1 ∩ C2 = C([725,46]) based on
- 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(3183, 728, F3, 46) (dual of [728, 545, 47]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(3196, 728, F3, 50) (dual of [728, 532, 51]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,46}, and designed minimum distance d ≥ |I|+1 = 51 [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(35, 18, F3, 3) (dual of [18, 13, 4]-code or 18-cap in PG(4,3)), 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(3201, 376, F3, 2, 50) (dual of [(376, 2), 551, 51]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3201, 188, F3, 4, 50) (dual of [(188, 4), 551, 51]-NRT-code) | [i] | ||