Information on Result #705544
Linear OA(3212, 765, F3, 52) (dual of [765, 553, 53]-code), using construction XX applied to C1 = C([337,385]), C2 = C([334,380]), C3 = C1 + C2 = C([337,380]), and C∩ = C1 ∩ C2 = C([334,385]) based on
- 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(3184, 728, F3, 47) (dual of [728, 544, 48]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {334,335,…,380}, and designed minimum distance d ≥ |I|+1 = 48 [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 = {334,335,…,385}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(3175, 728, F3, 44) (dual of [728, 553, 45]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,380}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(37, 25, F3, 4) (dual of [25, 18, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-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 OOA(3212, 382, F3, 2, 52) (dual of [(382, 2), 552, 53]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3212, 255, F3, 3, 52) (dual of [(255, 3), 553, 53]-NRT-code) | [i] | ||