Information on Result #1013815
Linear OOA(782, 3843230, F7, 3, 10) (dual of [(3843230, 3), 11529608, 11]-NRT-code), using (u, u+v)-construction based on
- linear OOA(78, 28, F7, 3, 5) (dual of [(28, 3), 76, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (3, 8, 28)-net over F7, using
- linear OOA(774, 3843202, F7, 3, 10) (dual of [(3843202, 3), 11529532, 11]-NRT-code), using
- trace code [i] based on linear OOA(4937, 1921601, F49, 3, 10) (dual of [(1921601, 3), 5764766, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4937, 5764803, F49, 10) (dual of [5764803, 5764766, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(4937, 5764805, F49, 10) (dual of [5764805, 5764768, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- 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(4933, 5764801, F49, 9) (dual of [5764801, 5764768, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(9) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(4937, 5764805, F49, 10) (dual of [5764805, 5764768, 11]-code), using
- OOA 3-folding [i] based on linear OA(4937, 5764803, F49, 10) (dual of [5764803, 5764766, 11]-code), using
- trace code [i] based on linear OOA(4937, 1921601, F49, 3, 10) (dual of [(1921601, 3), 5764766, 11]-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(782, 1921614, F7, 15, 10) (dual of [(1921614, 15), 28824128, 11]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |