Information on Result #675076
Linear OA(3216, 19755, F3, 33) (dual of [19755, 19539, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,12]) 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(3145, 19684, F3, 25) (dual of [19684, 19539, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(317, 71, F3, 7) (dual of [71, 54, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-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(3216, 12620, F3, 2, 33) (dual of [(12620, 2), 25024, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3216, 12620, F3, 3, 33) (dual of [(12620, 3), 37644, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(3216, 12620, F3, 4, 33) (dual of [(12620, 4), 50264, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(3216, 12620, F3, 5, 33) (dual of [(12620, 5), 62884, 34]-NRT-code) | [i] | ||
| 5 | Digital (183, 216, 12620)-net over F3 | [i] | ||
| 6 | Linear OOA(3216, 6585, F3, 3, 33) (dual of [(6585, 3), 19539, 34]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3216, 3951, F3, 5, 33) (dual of [(3951, 5), 19539, 34]-NRT-code) | [i] | ||