Information on Result #736949
Linear OA(3205, 19743, F3, 32) (dual of [19743, 19538, 33]-code), using construction X applied to Ce(31) ⊂ Ce(24) based on
- linear OA(3190, 19683, F3, 32) (dual of [19683, 19493, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(315, 60, F3, 6) (dual of [60, 45, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), 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 OA(3207, 19745, F3, 32) (dual of [19745, 19538, 33]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3208, 19746, F3, 32) (dual of [19746, 19538, 33]-code) | [i] | ||
| 3 | Linear OA(3209, 19747, F3, 32) (dual of [19747, 19538, 33]-code) | [i] | ||
| 4 | Linear OA(3210, 19748, F3, 32) (dual of [19748, 19538, 33]-code) | [i] | ||
| 5 | Linear OOA(3205, 10544, F3, 2, 32) (dual of [(10544, 2), 20883, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(3205, 10544, F3, 3, 32) (dual of [(10544, 3), 31427, 33]-NRT-code) | [i] | ||
| 7 | Linear OOA(3205, 10544, F3, 4, 32) (dual of [(10544, 4), 41971, 33]-NRT-code) | [i] | ||
| 8 | Linear OOA(3205, 10544, F3, 5, 32) (dual of [(10544, 5), 52515, 33]-NRT-code) | [i] | ||
| 9 | Digital (173, 205, 10544)-net over F3 | [i] | ||
| 10 | Linear OA(3209, 19748, F3, 32) (dual of [19748, 19539, 33]-code) | [i] | Construction X with Varšamov Bound | |
| 11 | Linear OOA(3205, 9871, F3, 2, 32) (dual of [(9871, 2), 19537, 33]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(3205, 6581, F3, 3, 32) (dual of [(6581, 3), 19538, 33]-NRT-code) | [i] | ||
| 13 | Linear OOA(3205, 4935, F3, 4, 32) (dual of [(4935, 4), 19535, 33]-NRT-code) | [i] | ||
| 14 | Linear OOA(3205, 3948, F3, 5, 32) (dual of [(3948, 5), 19535, 33]-NRT-code) | [i] | ||