Information on Result #705613
Linear OA(3204, 748, F3, 51) (dual of [748, 544, 52]-code), using construction XX applied to C1 = C([725,46]), C2 = C([0,48]), C3 = C1 + C2 = C([0,46]), and C∩ = C1 ∩ C2 = C([725,48]) based on
- 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(3190, 728, F3, 49) (dual of [728, 538, 50]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,48], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(3202, 728, F3, 52) (dual of [728, 526, 53]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,48}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(3184, 728, F3, 47) (dual of [728, 544, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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), 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 (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 OA(3205, 749, F3, 51) (dual of [749, 544, 52]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3204, 374, F3, 2, 51) (dual of [(374, 2), 544, 52]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3204, 249, F3, 3, 51) (dual of [(249, 3), 543, 52]-NRT-code) | [i] | ||
| 4 | Linear OOA(3204, 187, F3, 4, 51) (dual of [(187, 4), 544, 52]-NRT-code) | [i] | ||