Information on Result #678958
Linear OA(4176, 16420, F4, 32) (dual of [16420, 16244, 33]-code), using construction X applied to C([0,16]) ⊂ C([0,13]) based on
- linear OA(4169, 16385, F4, 33) (dual of [16385, 16216, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4141, 16385, F4, 27) (dual of [16385, 16244, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(47, 35, F4, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 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 OA(4177, 16421, F4, 32) (dual of [16421, 16244, 33]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4176, 13028, F4, 2, 32) (dual of [(13028, 2), 25880, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4176, 13028, F4, 3, 32) (dual of [(13028, 3), 38908, 33]-NRT-code) | [i] | ||
| 4 | Digital (144, 176, 13028)-net over F4 | [i] | ||
| 5 | Linear OA(4178, 16423, F4, 32) (dual of [16423, 16245, 33]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(4176, 8210, F4, 2, 32) (dual of [(8210, 2), 16244, 33]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4176, 5473, F4, 3, 32) (dual of [(5473, 3), 16243, 33]-NRT-code) | [i] | ||