Information on Result #678946
Linear OA(4218, 16420, F4, 40) (dual of [16420, 16202, 41]-code), using construction X applied to C([0,20]) ⊂ C([0,17]) based on
- linear OA(4211, 16385, F4, 41) (dual of [16385, 16174, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(4183, 16385, F4, 35) (dual of [16385, 16202, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (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(4219, 16421, F4, 40) (dual of [16421, 16202, 41]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4218, 13702, F4, 2, 40) (dual of [(13702, 2), 27186, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4218, 13702, F4, 3, 40) (dual of [(13702, 3), 40888, 41]-NRT-code) | [i] | ||
| 4 | Digital (178, 218, 13702)-net over F4 | [i] | ||
| 5 | Linear OA(4220, 16423, F4, 40) (dual of [16423, 16203, 41]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(4218, 8210, F4, 2, 40) (dual of [(8210, 2), 16202, 41]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4218, 5473, F4, 3, 40) (dual of [(5473, 3), 16201, 41]-NRT-code) | [i] | ||