Information on Result #704384
Linear OA(3104, 760, F3, 24) (dual of [760, 656, 25]-code), using construction XX applied to C1 = C([724,18]), C2 = C([1,19]), C3 = C1 + C2 = C([1,18]), and C∩ = C1 ∩ C2 = C([724,19]) based on
- linear OA(391, 728, F3, 23) (dual of [728, 637, 24]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,18}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(378, 728, F3, 19) (dual of [728, 650, 20]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(397, 728, F3, 24) (dual of [728, 631, 25]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,19}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(372, 728, F3, 18) (dual of [728, 656, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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]
- 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(3104, 756, F3, 2, 24) (dual of [(756, 2), 1408, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3104, 756, F3, 3, 24) (dual of [(756, 3), 2164, 25]-NRT-code) | [i] | ||
| 3 | Linear OOA(3104, 756, F3, 4, 24) (dual of [(756, 4), 2920, 25]-NRT-code) | [i] | ||
| 4 | Linear OOA(3104, 756, F3, 5, 24) (dual of [(756, 5), 3676, 25]-NRT-code) | [i] | ||
| 5 | Digital (80, 104, 756)-net over F3 | [i] | ||
| 6 | Linear OOA(3104, 380, F3, 2, 24) (dual of [(380, 2), 656, 25]-NRT-code) | [i] | OOA Folding | |