Information on Result #1011971
Linear OOA(4165, 2796267, F4, 3, 17) (dual of [(2796267, 3), 8388636, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(420, 66, F4, 3, 8) (dual of [(66, 3), 178, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 20, 66)-net over F4, using
- trace code for nets [i] based on digital (2, 10, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- trace code for nets [i] based on digital (2, 10, 33)-net over F16, using
- extracting embedded OOA [i] based on digital (12, 20, 66)-net over F4, using
- linear OOA(4145, 2796201, F4, 3, 17) (dual of [(2796201, 3), 8388458, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(4165, 2796267, F4, 3, 16) (dual of [(2796267, 3), 8388636, 17]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(4166, 2796267, F4, 3, 17) (dual of [(2796267, 3), 8388635, 18]-NRT-code) | [i] | OOA Duplication | |