Information on Result #1204716
Digital (49, 65, 1056895)-net over F256, using net defined by OOA based on linear OOA(25665, 1056895, F256, 20, 16) (dual of [(1056895, 20), 21137835, 17]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(25665, 2113791, F256, 4, 16) (dual of [(2113791, 4), 8455099, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(25619, 16641, F256, 4, 8) (dual of [(16641, 4), 66545, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2564, 257, F256, 4, 4) (dual of [(257, 4), 1024, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;1024,256) [i]
- linear OOA(25615, 16384, F256, 4, 8) (dual of [(16384, 4), 65521, 9]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OOA 4-folding [i] based on linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using
- linear OOA(2564, 257, F256, 4, 4) (dual of [(257, 4), 1024, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(25646, 2097150, F256, 4, 16) (dual of [(2097150, 4), 8388554, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25646, 8388600, F256, 16) (dual of [8388600, 8388554, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- OOA 4-folding [i] based on linear OA(25646, 8388600, F256, 16) (dual of [8388600, 8388554, 17]-code), using
- linear OOA(25619, 16641, F256, 4, 8) (dual of [(16641, 4), 66545, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
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 (244, 260, 4227580)-net over F4 | [i] | Trace Code for Nets | |
| 2 | Digital (114, 130, 2113790)-net over F16 | [i] | ||