Information on Result #679414
Linear OA(4113, 4113, F4, 25) (dual of [4113, 4000, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,10]) based on
- linear OA(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(497, 4097, F4, 21) (dual of [4097, 4000, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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(4113, 2668, F4, 2, 25) (dual of [(2668, 2), 5223, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4113, 2668, F4, 3, 25) (dual of [(2668, 3), 7891, 26]-NRT-code) | [i] | ||
| 3 | Digital (88, 113, 2668)-net over F4 | [i] | ||
| 4 | Linear OOA(4113, 2056, F4, 2, 25) (dual of [(2056, 2), 3999, 26]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4113, 1371, F4, 3, 25) (dual of [(1371, 3), 4000, 26]-NRT-code) | [i] | ||