Information on Result #1010921
Linear OOA(3248, 3188702, F3, 3, 18) (dual of [(3188702, 3), 9565858, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(324, 56, F3, 3, 9) (dual of [(56, 3), 144, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 24, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 12, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- trace code for nets [i] based on digital (3, 12, 28)-net over F9, using
- extracting embedded OOA [i] based on digital (15, 24, 56)-net over F3, using
- linear OOA(3224, 3188646, F3, 3, 18) (dual of [(3188646, 3), 9565714, 19]-NRT-code), using
- trace code [i] based on linear OOA(9112, 1594323, F9, 3, 18) (dual of [(1594323, 3), 4782857, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9112, 4782969, F9, 18) (dual of [4782969, 4782857, 19]-code), using
- 1 times truncation [i] based on linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using
- OOA 3-folding [i] based on linear OA(9112, 4782969, F9, 18) (dual of [4782969, 4782857, 19]-code), using
- trace code [i] based on linear OOA(9112, 1594323, F9, 3, 18) (dual of [(1594323, 3), 4782857, 19]-NRT-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(3249, 3188702, F3, 3, 18) (dual of [(3188702, 3), 9565857, 19]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3248, 1062900, F3, 21, 18) (dual of [(1062900, 21), 22320652, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |