Information on Result #678538
Linear OA(4196, 65556, F4, 32) (dual of [65556, 65360, 33]-code), using construction X applied to C([0,16]) ⊂ C([0,14]) based on
- linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4177, 65537, F4, 29) (dual of [65537, 65360, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(43, 19, F4, 2) (dual of [19, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-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(4196, 32866, F4, 2, 32) (dual of [(32866, 2), 65536, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4196, 32866, F4, 3, 32) (dual of [(32866, 3), 98402, 33]-NRT-code) | [i] | ||
| 3 | Digital (164, 196, 32866)-net over F4 | [i] | ||
| 4 | Linear OOA(4196, 32778, F4, 2, 32) (dual of [(32778, 2), 65360, 33]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4196, 21852, F4, 3, 32) (dual of [(21852, 3), 65360, 33]-NRT-code) | [i] | ||