Information on Result #1022010
Linear OOA(8118, 5592735, F8, 3, 13) (dual of [(5592735, 3), 16778087, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(820, 333, F8, 3, 6) (dual of [(333, 3), 979, 7]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(83, 73, F8, 3, 2) (dual of [(73, 3), 216, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(83, 73, F8, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
- appending kth column [i] based on linear OA(83, 73, F8, 2) (dual of [73, 70, 3]-code), using
- Hamming code H(3,8) [i]
- appending kth column [i] based on linear OA(83, 73, F8, 2) (dual of [73, 70, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(83, 73, F8, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
- linear OOA(85, 130, F8, 3, 3) (dual of [(130, 3), 385, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(85, 207, F8, 3, 3) (dual of [(207, 3), 616, 4]-NRT-code), using
- linear OOA(812, 130, F8, 3, 6) (dual of [(130, 3), 378, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 12, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 6, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 6, 65)-net over F64, using
- extracting embedded OOA [i] based on digital (6, 12, 130)-net over F8, using
- linear OOA(83, 73, F8, 3, 2) (dual of [(73, 3), 216, 3]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(898, 5592402, F8, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
- trace code [i] based on linear OOA(6449, 2796201, F64, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6449, large, F64, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6449, large, F64, 13) (dual of [large, large−49, 14]-code), using
- trace code [i] based on linear OOA(6449, 2796201, F64, 3, 13) (dual of [(2796201, 3), 8388554, 14]-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(8118, 2796367, F8, 15, 13) (dual of [(2796367, 15), 41945387, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |