Information on Result #704435
Linear OA(392, 741, F3, 23) (dual of [741, 649, 24]-code), using construction XX applied to C1 = C([343,364]), C2 = C([345,365]), C3 = C1 + C2 = C([345,364]), and C∩ = C1 ∩ C2 = C([343,365]) based on
- linear OA(385, 728, F3, 22) (dual of [728, 643, 23]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {343,344,…,364}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(385, 728, F3, 21) (dual of [728, 643, 22]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {345,346,…,365}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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 = {343,344,…,365}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(379, 728, F3, 20) (dual of [728, 649, 21]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {345,346,…,364}, and designed minimum distance d ≥ |I|+1 = 21 [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(392, 489, F3, 2, 23) (dual of [(489, 2), 886, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(392, 489, F3, 3, 23) (dual of [(489, 3), 1375, 24]-NRT-code) | [i] | ||
| 3 | Linear OOA(392, 489, F3, 4, 23) (dual of [(489, 4), 1864, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(392, 489, F3, 5, 23) (dual of [(489, 5), 2353, 24]-NRT-code) | [i] | ||
| 5 | Digital (69, 92, 489)-net over F3 | [i] | ||
| 6 | Linear OA(3100, 770, F3, 23) (dual of [770, 670, 24]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(3101, 783, F3, 23) (dual of [783, 682, 24]-code) | [i] | ||
| 8 | Linear OA(3102, 799, F3, 23) (dual of [799, 697, 24]-code) | [i] | ||
| 9 | Linear OA(3103, 821, F3, 23) (dual of [821, 718, 24]-code) | [i] | ||
| 10 | Linear OA(3104, 848, F3, 23) (dual of [848, 744, 24]-code) | [i] | ||
| 11 | Linear OOA(392, 370, F3, 2, 23) (dual of [(370, 2), 648, 24]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(392, 247, F3, 3, 23) (dual of [(247, 3), 649, 24]-NRT-code) | [i] | ||
| 13 | Linear OOA(392, 185, F3, 4, 23) (dual of [(185, 4), 648, 24]-NRT-code) | [i] | ||