Information on Result #1021993
Linear OOA(7109, 3843410, F7, 3, 12) (dual of [(3843410, 3), 11530121, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(719, 208, F7, 3, 6) (dual of [(208, 3), 605, 7]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(72, 8, F7, 3, 2) (dual of [(8, 3), 22, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;22,7) [i]
- linear OOA(75, 100, F7, 3, 3) (dual of [(100, 3), 295, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(75, 131, F7, 3, 3) (dual of [(131, 3), 388, 4]-NRT-code), using
- linear OOA(712, 100, F7, 3, 6) (dual of [(100, 3), 288, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 12, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 6, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- trace code for nets [i] based on digital (0, 6, 50)-net over F49, using
- extracting embedded OOA [i] based on digital (6, 12, 100)-net over F7, using
- linear OOA(72, 8, F7, 3, 2) (dual of [(8, 3), 22, 3]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(790, 3843202, F7, 3, 12) (dual of [(3843202, 3), 11529516, 13]-NRT-code), using
- trace code [i] based on linear OOA(4945, 1921601, F49, 3, 12) (dual of [(1921601, 3), 5764758, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4945, 5764803, F49, 12) (dual of [5764803, 5764758, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4945, 5764805, F49, 12) (dual of [5764805, 5764760, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4941, 5764801, F49, 11) (dual of [5764801, 5764760, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(4945, 5764805, F49, 12) (dual of [5764805, 5764760, 13]-code), using
- OOA 3-folding [i] based on linear OA(4945, 5764803, F49, 12) (dual of [5764803, 5764758, 13]-code), using
- trace code [i] based on linear OOA(4945, 1921601, F49, 3, 12) (dual of [(1921601, 3), 5764758, 13]-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(7109, 1921704, F7, 15, 12) (dual of [(1921704, 15), 28825451, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |