Information on Result #704748
Linear OA(3143, 759, F3, 35) (dual of [759, 616, 36]-code), using construction XX applied to C1 = C([331,364]), C2 = C([336,365]), C3 = C1 + C2 = C([336,364]), and C∩ = C1 ∩ C2 = C([331,365]) based on
- 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 = {331,332,…,364}, 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(3136, 728, F3, 35) (dual of [728, 592, 36]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {331,332,…,365}, and designed minimum distance d ≥ |I|+1 = 36 [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(37, 25, F3, 4) (dual of [25, 18, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), 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(3143, 715, F3, 2, 35) (dual of [(715, 2), 1287, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3143, 715, F3, 3, 35) (dual of [(715, 3), 2002, 36]-NRT-code) | [i] | ||
| 3 | Linear OOA(3143, 715, F3, 4, 35) (dual of [(715, 4), 2717, 36]-NRT-code) | [i] | ||
| 4 | Linear OOA(3143, 715, F3, 5, 35) (dual of [(715, 5), 3432, 36]-NRT-code) | [i] | ||
| 5 | Digital (108, 143, 715)-net over F3 | [i] | ||
| 6 | Linear OOA(3143, 379, F3, 2, 35) (dual of [(379, 2), 615, 36]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3143, 253, F3, 3, 35) (dual of [(253, 3), 616, 36]-NRT-code) | [i] | ||
| 8 | Linear OOA(3143, 189, F3, 4, 35) (dual of [(189, 4), 613, 36]-NRT-code) | [i] | ||