Information on Result #704770
Linear OA(3137, 756, F3, 34) (dual of [756, 619, 35]-code), using construction XX applied to C1 = C([725,27]), C2 = C([0,30]), C3 = C1 + C2 = C([0,27]), and C∩ = C1 ∩ C2 = C([725,30]) based on
- linear OA(3121, 728, F3, 31) (dual of [728, 607, 32]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,27}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3118, 728, F3, 31) (dual of [728, 610, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3130, 728, F3, 34) (dual of [728, 598, 35]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,30}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3109, 728, F3, 28) (dual of [728, 619, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(34, 16, F3, 2) (dual of [16, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-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(3137, 378, F3, 2, 34) (dual of [(378, 2), 619, 35]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3137, 252, F3, 3, 34) (dual of [(252, 3), 619, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(3137, 189, F3, 4, 34) (dual of [(189, 4), 619, 35]-NRT-code) | [i] | ||