Information on Result #675033
Linear OA(3244, 19729, F3, 38) (dual of [19729, 19485, 39]-code), using construction X applied to C([0,19]) ⊂ C([0,16]) based on
- linear OA(3235, 19684, F3, 39) (dual of [19684, 19449, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(3199, 19684, F3, 33) (dual of [19684, 19485, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [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, 11830, F3, 2, 38) (dual of [(11830, 2), 23416, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3244, 11830, F3, 3, 38) (dual of [(11830, 3), 35246, 39]-NRT-code) | [i] | ||
| 3 | Linear OOA(3244, 11830, F3, 4, 38) (dual of [(11830, 4), 47076, 39]-NRT-code) | [i] | ||
| 4 | Linear OOA(3244, 11830, F3, 5, 38) (dual of [(11830, 5), 58906, 39]-NRT-code) | [i] | ||
| 5 | Digital (206, 244, 11830)-net over F3 | [i] | ||