Information on Result #1013925
Linear OOA(7105, 3843215, F7, 3, 13) (dual of [(3843215, 3), 11529540, 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(798, 3843202, F7, 3, 13) (dual of [(3843202, 3), 11529508, 14]-NRT-code), using
- trace code [i] based on linear OOA(4949, 1921601, F49, 3, 13) (dual of [(1921601, 3), 5764754, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4949, 5764803, F49, 13) (dual of [5764803, 5764754, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4949, 5764805, F49, 13) (dual of [5764805, 5764756, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(4949, 5764801, F49, 13) (dual of [5764801, 5764752, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 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(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(12) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(4949, 5764805, F49, 13) (dual of [5764805, 5764756, 14]-code), using
- OOA 3-folding [i] based on linear OA(4949, 5764803, F49, 13) (dual of [5764803, 5764754, 14]-code), using
- trace code [i] based on linear OOA(4949, 1921601, F49, 3, 13) (dual of [(1921601, 3), 5764754, 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(7105, 1921607, F7, 15, 13) (dual of [(1921607, 15), 28824000, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |