Information on Result #705688
Linear OA(3222, 757, F3, 56) (dual of [757, 535, 57]-code), using construction XX applied to C1 = C([337,391]), C2 = C([336,385]), C3 = C1 + C2 = C([337,385]), and C∩ = C1 ∩ C2 = C([336,391]) based on
- linear OA(3211, 728, F3, 55) (dual of [728, 517, 56]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,391}, and designed minimum distance d ≥ |I|+1 = 56 [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 = {336,337,…,385}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- 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 = {336,337,…,391}, and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(3193, 728, F3, 49) (dual of [728, 535, 50]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,385}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- 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
- linear OA(30, 3, F3, 0) (dual of [3, 3, 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 OA(3223, 758, F3, 56) (dual of [758, 535, 57]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3225, 760, F3, 56) (dual of [760, 535, 57]-code) | [i] | ||
| 3 | Linear OOA(3222, 378, F3, 2, 56) (dual of [(378, 2), 534, 57]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3222, 252, F3, 3, 56) (dual of [(252, 3), 534, 57]-NRT-code) | [i] | ||
| 5 | Linear OOA(3222, 189, F3, 4, 56) (dual of [(189, 4), 534, 57]-NRT-code) | [i] | ||