Information on Result #704180
Linear OA(354, 757, F3, 12) (dual of [757, 703, 13]-code), using construction XX applied to C1 = C([725,6]), C2 = C([0,9]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([725,9]) based on
- linear OA(337, 728, F3, 10) (dual of [728, 691, 11]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,6}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(337, 728, F3, 10) (dual of [728, 691, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(349, 728, F3, 13) (dual of [728, 679, 14]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,9}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(325, 728, F3, 7) (dual of [728, 703, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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
- 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
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(354, 756, F3, 2, 12) (dual of [(756, 2), 1458, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(354, 756, F3, 3, 12) (dual of [(756, 3), 2214, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(354, 756, F3, 4, 12) (dual of [(756, 4), 2970, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(354, 756, F3, 5, 12) (dual of [(756, 5), 3726, 13]-NRT-code) | [i] | ||
| 5 | Digital (42, 54, 756)-net over F3 | [i] | ||
| 6 | Linear OOA(354, 378, F3, 2, 12) (dual of [(378, 2), 702, 13]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(354, 252, F3, 3, 12) (dual of [(252, 3), 702, 13]-NRT-code) | [i] | ||