Information on Result #704599
Linear OA(3122, 748, F3, 30) (dual of [748, 626, 31]-code), using construction XX applied to C1 = C([336,363]), C2 = C([339,365]), C3 = C1 + C2 = C([339,363]), and C∩ = C1 ∩ C2 = C([336,365]) based on
- linear OA(3111, 728, F3, 28) (dual of [728, 617, 29]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,363}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3109, 728, F3, 27) (dual of [728, 619, 28]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {339,340,…,365}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3118, 728, F3, 30) (dual of [728, 610, 31]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,365}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3102, 728, F3, 25) (dual of [728, 626, 26]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {339,340,…,363}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- 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
- linear OA(31, 8, F3, 1) (dual of [8, 7, 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(3122, 374, F3, 2, 30) (dual of [(374, 2), 626, 31]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3122, 249, F3, 3, 30) (dual of [(249, 3), 625, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(3122, 187, F3, 4, 30) (dual of [(187, 4), 626, 31]-NRT-code) | [i] | ||