Information on Result #704832
Linear OA(3132, 742, F3, 34) (dual of [742, 610, 35]-code), using construction XX applied to C1 = C([336,367]), C2 = C([334,365]), C3 = C1 + C2 = C([336,365]), and C∩ = C1 ∩ C2 = C([334,367]) based on
- linear OA(3124, 728, F3, 32) (dual of [728, 604, 33]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,367}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3124, 728, F3, 32) (dual of [728, 604, 33]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {334,335,…,365}, and designed minimum distance d ≥ |I|+1 = 33 [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 = {334,335,…,367}, and designed minimum distance d ≥ |I|+1 = 35 [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(31, 7, F3, 1) (dual of [7, 6, 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(31, 7, F3, 1) (dual of [7, 6, 2]-code) (see above)
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(3133, 743, F3, 34) (dual of [743, 610, 35]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3140, 766, F3, 34) (dual of [766, 626, 35]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(3141, 775, F3, 34) (dual of [775, 634, 35]-code) | [i] | ||
| 4 | Linear OA(3142, 787, F3, 34) (dual of [787, 645, 35]-code) | [i] | ||
| 5 | Linear OA(3143, 803, F3, 34) (dual of [803, 660, 35]-code) | [i] | ||
| 6 | Linear OOA(3132, 371, F3, 2, 34) (dual of [(371, 2), 610, 35]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3132, 247, F3, 3, 34) (dual of [(247, 3), 609, 35]-NRT-code) | [i] | ||
| 8 | Linear OOA(3132, 185, F3, 4, 34) (dual of [(185, 4), 608, 35]-NRT-code) | [i] | ||
| 9 | Linear OOA(3132, 148, F3, 5, 34) (dual of [(148, 5), 608, 35]-NRT-code) | [i] | ||