Information on Result #704777
Linear OA(3132, 748, F3, 33) (dual of [748, 616, 34]-code), using construction XX applied to C1 = C([725,28]), C2 = C([0,30]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([725,30]) 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 = {−3,−2,…,28}, and designed minimum distance d ≥ |I|+1 = 33 [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(3112, 728, F3, 29) (dual of [728, 616, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [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(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 (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, 749, F3, 33) (dual of [749, 616, 34]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3132, 618, F3, 2, 33) (dual of [(618, 2), 1104, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3132, 618, F3, 3, 33) (dual of [(618, 3), 1722, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(3132, 618, F3, 4, 33) (dual of [(618, 4), 2340, 34]-NRT-code) | [i] | ||
| 5 | Linear OOA(3132, 618, F3, 5, 33) (dual of [(618, 5), 2958, 34]-NRT-code) | [i] | ||
| 6 | Digital (99, 132, 618)-net over F3 | [i] | ||
| 7 | Linear OA(3136, 758, F3, 33) (dual of [758, 622, 34]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OOA(3132, 374, F3, 2, 33) (dual of [(374, 2), 616, 34]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(3132, 249, F3, 3, 33) (dual of [(249, 3), 615, 34]-NRT-code) | [i] | ||
| 10 | Linear OOA(3132, 187, F3, 4, 33) (dual of [(187, 4), 616, 34]-NRT-code) | [i] | ||