Information on Result #704573
Linear OA(3124, 756, F3, 30) (dual of [756, 632, 31]-code), using construction XX applied to C1 = C([336,363]), C2 = C([340,365]), C3 = C1 + C2 = C([340,363]), 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(3103, 728, F3, 26) (dual of [728, 625, 27]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {340,341,…,365}, and designed minimum distance d ≥ |I|+1 = 27 [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(396, 728, F3, 24) (dual of [728, 632, 25]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {340,341,…,363}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(35, 20, F3, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), 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 OA(3125, 757, F3, 30) (dual of [757, 632, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3124, 378, F3, 2, 30) (dual of [(378, 2), 632, 31]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3124, 252, F3, 3, 30) (dual of [(252, 3), 632, 31]-NRT-code) | [i] | ||