Information on Result #896330
Linear OOA(786, 5764912, F7, 2, 10) (dual of [(5764912, 2), 11529738, 11]-NRT-code), using (u, u+v)-construction based on
- linear OOA(712, 108, F7, 2, 5) (dual of [(108, 2), 204, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(72, 8, F7, 2, 2) (dual of [(8, 2), 14, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;14,7) [i]
- linear OOA(710, 100, F7, 2, 5) (dual of [(100, 2), 190, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 10, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 5, 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, 5, 50)-net over F49, using
- extracting embedded OOA [i] based on digital (5, 10, 100)-net over F7, using
- linear OOA(72, 8, F7, 2, 2) (dual of [(8, 2), 14, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(774, 5764804, F7, 2, 10) (dual of [(5764804, 2), 11529534, 11]-NRT-code), using
- trace code [i] based on linear OOA(4937, 2882402, F49, 2, 10) (dual of [(2882402, 2), 5764767, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4937, 5764804, F49, 10) (dual of [5764804, 5764767, 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 2-folding [i] based on linear OA(4937, 5764804, F49, 10) (dual of [5764804, 5764767, 11]-code), using
- trace code [i] based on linear OOA(4937, 2882402, F49, 2, 10) (dual of [(2882402, 2), 5764767, 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(786, 2882456, F7, 3, 10) (dual of [(2882456, 3), 8647282, 11]-NRT-code) | [i] | OOA Folding | |