Information on Result #704737
Linear OA(3125, 741, F3, 32) (dual of [741, 616, 33]-code), using construction XX applied to C1 = C([334,364]), C2 = C([336,365]), C3 = C1 + C2 = C([336,364]), and C∩ = C1 ∩ C2 = C([334,365]) based on
- linear OA(3118, 728, F3, 31) (dual of [728, 610, 32]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {334,335,…,364}, and designed minimum distance d ≥ |I|+1 = 32 [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(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(3112, 728, F3, 29) (dual of [728, 616, 30]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,364}, and designed minimum distance d ≥ |I|+1 = 30 [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(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-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 OOA(3125, 539, F3, 2, 32) (dual of [(539, 2), 953, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3125, 539, F3, 3, 32) (dual of [(539, 3), 1492, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(3125, 539, F3, 4, 32) (dual of [(539, 4), 2031, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(3125, 539, F3, 5, 32) (dual of [(539, 5), 2570, 33]-NRT-code) | [i] | ||
| 5 | Digital (93, 125, 539)-net over F3 | [i] | ||
| 6 | Linear OA(3133, 766, F3, 32) (dual of [766, 633, 33]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(3134, 776, F3, 32) (dual of [776, 642, 33]-code) | [i] | ||
| 8 | Linear OA(3135, 788, F3, 32) (dual of [788, 653, 33]-code) | [i] | ||
| 9 | Linear OA(3136, 804, F3, 32) (dual of [804, 668, 33]-code) | [i] | ||
| 10 | Linear OA(3137, 824, F3, 32) (dual of [824, 687, 33]-code) | [i] | ||
| 11 | Linear OA(3138, 848, F3, 32) (dual of [848, 710, 33]-code) | [i] | ||
| 12 | Linear OA(3139, 875, F3, 32) (dual of [875, 736, 33]-code) | [i] | ||
| 13 | Linear OA(3140, 904, F3, 32) (dual of [904, 764, 33]-code) | [i] | ||
| 14 | Linear OA(3141, 935, F3, 32) (dual of [935, 794, 33]-code) | [i] | ||
| 15 | Linear OA(3142, 968, F3, 32) (dual of [968, 826, 33]-code) | [i] | ||
| 16 | Linear OA(3143, 1002, F3, 32) (dual of [1002, 859, 33]-code) | [i] | ||
| 17 | Linear OOA(3125, 370, F3, 2, 32) (dual of [(370, 2), 615, 33]-NRT-code) | [i] | OOA Folding | |
| 18 | Linear OOA(3125, 247, F3, 3, 32) (dual of [(247, 3), 616, 33]-NRT-code) | [i] | ||
| 19 | Linear OOA(3125, 185, F3, 4, 32) (dual of [(185, 4), 615, 33]-NRT-code) | [i] | ||
| 20 | Linear OOA(3125, 148, F3, 5, 32) (dual of [(148, 5), 615, 33]-NRT-code) | [i] | ||