Information on Result #1013905
Linear OOA(7104, 3843306, F7, 3, 12) (dual of [(3843306, 3), 11529814, 13]-NRT-code), using (u, u+v)-construction based on
- 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(792, 3843206, F7, 3, 12) (dual of [(3843206, 3), 11529526, 13]-NRT-code), using
- trace code [i] based on linear OOA(4946, 1921603, F49, 3, 12) (dual of [(1921603, 3), 5764763, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4946, 5764809, F49, 12) (dual of [5764809, 5764763, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4946, 5764810, F49, 12) (dual of [5764810, 5764764, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [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(4937, 5764801, F49, 10) (dual of [5764801, 5764764, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(491, 9, F49, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(4946, 5764810, F49, 12) (dual of [5764810, 5764764, 13]-code), using
- OOA 3-folding [i] based on linear OA(4946, 5764809, F49, 12) (dual of [5764809, 5764763, 13]-code), using
- trace code [i] based on linear OOA(4946, 1921603, F49, 3, 12) (dual of [(1921603, 3), 5764763, 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(7104, 1921652, F7, 15, 12) (dual of [(1921652, 15), 28824676, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |