Information on Result #679402
Linear OA(4185, 4113, F4, 41) (dual of [4113, 3928, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,18]) based on
- linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(4169, 4097, F4, 37) (dual of [4097, 3928, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(44, 16, F4, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,4)), 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(4185, 3524, F4, 2, 41) (dual of [(3524, 2), 6863, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4185, 3524, F4, 3, 41) (dual of [(3524, 3), 10387, 42]-NRT-code) | [i] | ||
| 3 | Digital (144, 185, 3524)-net over F4 | [i] | ||
| 4 | Linear OOA(4185, 2056, F4, 2, 41) (dual of [(2056, 2), 3927, 42]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4185, 1371, F4, 3, 41) (dual of [(1371, 3), 3928, 42]-NRT-code) | [i] | ||