Information on Result #895645
Linear OOA(4189, 4194349, F4, 2, 19) (dual of [(4194349, 2), 8388509, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(420, 48, F4, 2, 9) (dual of [(48, 2), 76, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (11, 20, 48)-net over F4, using
- trace code for nets [i] based on digital (1, 10, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- trace code for nets [i] based on digital (1, 10, 24)-net over F16, using
- extracting embedded OOA [i] based on digital (11, 20, 48)-net over F4, using
- linear OOA(4169, 4194301, F4, 2, 19) (dual of [(4194301, 2), 8388433, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4169, 8388602, F4, 19) (dual of [8388602, 8388433, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4169, large, F4, 19) (dual of [large, large−169, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4169, large, F4, 19) (dual of [large, large−169, 20]-code), using
- OOA 2-folding [i] based on linear OA(4169, 8388602, F4, 19) (dual of [8388602, 8388433, 20]-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(4190, 4194349, F4, 2, 19) (dual of [(4194349, 2), 8388508, 20]-NRT-code) | [i] | OOA Duplication | |