Information on Result #895585
Linear OOA(4164, 4194367, F4, 2, 16) (dual of [(4194367, 2), 8388570, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(420, 66, F4, 2, 8) (dual of [(66, 2), 112, 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(4144, 4194301, F4, 2, 16) (dual of [(4194301, 2), 8388458, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4144, 8388602, F4, 16) (dual of [8388602, 8388458, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4144, large, F4, 16) (dual of [large, large−144, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(4144, large, F4, 16) (dual of [large, large−144, 17]-code), using
- OOA 2-folding [i] based on linear OA(4144, 8388602, F4, 16) (dual of [8388602, 8388458, 17]-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(4164, 1048591, F4, 18, 16) (dual of [(1048591, 18), 18874474, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |