Information on Result #1081292
Linear OOA(3192, 2097235, F3, 4, 17) (dual of [(2097235, 4), 8388748, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(324, 84, F3, 4, 8) (dual of [(84, 4), 312, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 24, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 8, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- trace code for nets [i] based on digital (0, 8, 28)-net over F27, using
- extracting embedded OOA [i] based on digital (16, 24, 84)-net over F3, using
- linear OOA(3168, 2097151, F3, 4, 17) (dual of [(2097151, 4), 8388436, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3168, 4194302, F3, 2, 17) (dual of [(4194302, 2), 8388436, 18]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3166, 4194301, F3, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3166, 8388602, F3, 17) (dual of [8388602, 8388436, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- OOA 2-folding [i] based on linear OA(3166, 8388602, F3, 17) (dual of [8388602, 8388436, 18]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3166, 4194301, F3, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3168, 4194302, F3, 2, 17) (dual of [(4194302, 2), 8388436, 18]-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(3192, 1048617, F3, 20, 17) (dual of [(1048617, 20), 20972148, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |