Information on Result #705797
Linear OA(3234, 763, F3, 59) (dual of [763, 529, 60]-code), using construction XX applied to C1 = C([337,392]), C2 = C([334,386]), C3 = C1 + C2 = C([337,386]), and C∩ = C1 ∩ C2 = C([334,392]) based on
- linear OA(3214, 728, F3, 56) (dual of [728, 514, 57]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,392}, and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(3208, 728, F3, 53) (dual of [728, 520, 54]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {334,335,…,386}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(3223, 728, F3, 59) (dual of [728, 505, 60]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {334,335,…,392}, and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(3199, 728, F3, 50) (dual of [728, 529, 51]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,386}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(38, 23, F3, 5) (dual of [23, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 26, F3, 5) (dual of [26, 18, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- discarding factors / shortening the dual code based on linear OA(38, 26, F3, 5) (dual of [26, 18, 6]-code), using
- linear OA(33, 12, F3, 2) (dual of [12, 9, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), 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 OA(3235, 764, F3, 59) (dual of [764, 529, 60]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3236, 765, F3, 59) (dual of [765, 529, 60]-code) | [i] | ||
| 3 | Linear OOA(3234, 381, F3, 2, 59) (dual of [(381, 2), 528, 60]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3234, 254, F3, 3, 59) (dual of [(254, 3), 528, 60]-NRT-code) | [i] | ||