Information on Result #1200472
Digital (41, 50, 2883602)-net over F49, using net defined by OOA based on linear OOA(4950, 2883602, F49, 10, 9) (dual of [(2883602, 10), 28835970, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(4950, 5767205, F49, 2, 9) (dual of [(5767205, 2), 11534360, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4950, 5767206, F49, 2, 9) (dual of [(5767206, 2), 11534362, 10]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(494, 2402, F49, 2, 3) (dual of [(2402, 2), 4800, 4]-NRT-code), using
- linear OOA(4913, 2882402, F49, 2, 4) (dual of [(2882402, 2), 5764791, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4913, 5764804, F49, 4) (dual of [5764804, 5764791, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(499, 5764801, F49, 3) (dual of [5764801, 5764792, 4]-code or 5764801-cap in PG(8,49)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using
- OOA 2-folding [i] based on linear OA(4913, 5764804, F49, 4) (dual of [5764804, 5764791, 5]-code), using
- 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) (see above)
- 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
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(4950, 5767206, F49, 2, 9) (dual of [(5767206, 2), 11534362, 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, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (91, 100, 5767204)-net over F7 | [i] | Trace Code for Nets | |