Information on Result #896319
Linear OOA(773, 5764854, F7, 2, 9) (dual of [(5764854, 2), 11529635, 10]-NRT-code), using (u, u+v)-construction based on
- linear OOA(77, 50, F7, 2, 4) (dual of [(50, 2), 93, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (3, 7, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(3,49) in PG(6,7)) for nets [i] based on digital (0, 4, 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
- base reduction for projective spaces (embedding PG(3,49) in PG(6,7)) for nets [i] based on digital (0, 4, 50)-net over F49, using
- extracting embedded OOA [i] based on digital (3, 7, 50)-net over F7, using
- linear OOA(766, 5764804, F7, 2, 9) (dual of [(5764804, 2), 11529542, 10]-NRT-code), using
- trace code [i] based on linear OOA(4933, 2882402, F49, 2, 9) (dual of [(2882402, 2), 5764771, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4933, 5764804, F49, 9) (dual of [5764804, 5764771, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(4933, 5764805, F49, 9) (dual of [5764805, 5764772, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- 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(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(8) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(4933, 5764805, F49, 9) (dual of [5764805, 5764772, 10]-code), using
- OOA 2-folding [i] based on linear OA(4933, 5764804, F49, 9) (dual of [5764804, 5764771, 10]-code), using
- trace code [i] based on linear OOA(4933, 2882402, F49, 2, 9) (dual of [(2882402, 2), 5764771, 10]-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(773, 2882427, F7, 3, 9) (dual of [(2882427, 3), 8647208, 10]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(773, 2882426, F7, 10, 9) (dual of [(2882426, 10), 28824187, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |