Information on Result #824057
Linear OOA(4189, 524312, F4, 2, 24) (dual of [(524312, 2), 1048435, 25]-NRT-code), using OOA 2-folding based on linear OA(4189, 1048624, F4, 24) (dual of [1048624, 1048435, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4189, 1048625, F4, 24) (dual of [1048625, 1048436, 25]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(4181, 1048577, F4, 25) (dual of [1048577, 1048396, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(4141, 1048577, F4, 19) (dual of [1048577, 1048436, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(48, 48, F4, 4) (dual of [48, 40, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
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(4189, 524312, F4, 3, 24) (dual of [(524312, 3), 1572747, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (165, 189, 524312)-net over F4 | [i] | ||