Information on Result #675047
Linear OA(3208, 19729, F3, 32) (dual of [19729, 19521, 33]-code), using construction X applied to C([0,16]) ⊂ C([0,13]) based on
- 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(3163, 19684, F3, 27) (dual of [19684, 19521, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (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(3208, 11772, F3, 2, 32) (dual of [(11772, 2), 23336, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3208, 11772, F3, 3, 32) (dual of [(11772, 3), 35108, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(3208, 11772, F3, 4, 32) (dual of [(11772, 4), 46880, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(3208, 11772, F3, 5, 32) (dual of [(11772, 5), 58652, 33]-NRT-code) | [i] | ||
| 5 | Digital (176, 208, 11772)-net over F3 | [i] | ||