Information on Result #895620
Linear OOA(4175, 4194335, F4, 2, 18) (dual of [(4194335, 2), 8388495, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(418, 34, F4, 2, 9) (dual of [(34, 2), 50, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (9, 18, 34)-net over F4, using
- trace code for nets [i] based on digital (0, 9, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- trace code for nets [i] based on digital (0, 9, 17)-net over F16, using
- extracting embedded OOA [i] based on digital (9, 18, 34)-net over F4, using
- linear OOA(4157, 4194301, F4, 2, 18) (dual of [(4194301, 2), 8388445, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4157, 8388602, F4, 18) (dual of [8388602, 8388445, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- OOA 2-folding [i] based on linear OA(4157, 8388602, F4, 18) (dual of [8388602, 8388445, 19]-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(4176, 4194335, F4, 2, 18) (dual of [(4194335, 2), 8388494, 19]-NRT-code) | [i] | OOA Duplication | |