Information on Result #1013930
Linear OOA(7107, 3843219, F7, 3, 13) (dual of [(3843219, 3), 11529550, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(77, 13, F7, 3, 6) (dual of [(13, 3), 32, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 7, 13)-net over F7, using
- 6 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- extracting embedded OOA [i] based on digital (1, 7, 13)-net over F7, using
- linear OOA(7100, 3843206, F7, 3, 13) (dual of [(3843206, 3), 11529518, 14]-NRT-code), using
- trace code [i] based on linear OOA(4950, 1921603, F49, 3, 13) (dual of [(1921603, 3), 5764759, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4950, 5764809, F49, 13) (dual of [5764809, 5764759, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4950, 5764811, F49, 13) (dual of [5764811, 5764761, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(4949, 5764802, F49, 13) (dual of [5764802, 5764753, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(4941, 5764802, F49, 11) (dual of [5764802, 5764761, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [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 C([0,6]) ⊂ C([0,5]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4950, 5764811, F49, 13) (dual of [5764811, 5764761, 14]-code), using
- OOA 3-folding [i] based on linear OA(4950, 5764809, F49, 13) (dual of [5764809, 5764759, 14]-code), using
- trace code [i] based on linear OOA(4950, 1921603, F49, 3, 13) (dual of [(1921603, 3), 5764759, 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(7107, 1921609, F7, 15, 13) (dual of [(1921609, 15), 28824028, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |