Information on Result #675206
Linear OA(3244, 19728, F3, 39) (dual of [19728, 19484, 40]-code), using construction X applied to Ce(39) ⊂ Ce(33) based on
- linear OA(3235, 19683, F3, 40) (dual of [19683, 19448, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3199, 19683, F3, 34) (dual of [19683, 19484, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(39, 45, F3, 4) (dual of [45, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-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 OOA(3244, 9928, F3, 2, 39) (dual of [(9928, 2), 19612, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3244, 9928, F3, 3, 39) (dual of [(9928, 3), 29540, 40]-NRT-code) | [i] | ||
| 3 | Linear OOA(3244, 9928, F3, 4, 39) (dual of [(9928, 4), 39468, 40]-NRT-code) | [i] | ||
| 4 | Linear OOA(3244, 9928, F3, 5, 39) (dual of [(9928, 5), 49396, 40]-NRT-code) | [i] | ||
| 5 | Digital (205, 244, 9928)-net over F3 | [i] | ||
| 6 | Linear OOA(3244, 9864, F3, 2, 39) (dual of [(9864, 2), 19484, 40]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3244, 6576, F3, 3, 39) (dual of [(6576, 3), 19484, 40]-NRT-code) | [i] | ||
| 8 | Linear OOA(3244, 4932, F3, 4, 39) (dual of [(4932, 4), 19484, 40]-NRT-code) | [i] | ||
| 9 | Linear OOA(3244, 3945, F3, 5, 39) (dual of [(3945, 5), 19481, 40]-NRT-code) | [i] | ||