Information on Result #1221047
Digital (52, 63, 1678921)-net over F25, using (u, u+v)-construction based on
- digital (7, 12, 1201)-net over F25, using
- net defined by OOA [i] based on linear OOA(2512, 1201, F25, 5, 5) (dual of [(1201, 5), 5993, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2512, 2403, F25, 5) (dual of [2403, 2391, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(2512, 2404, F25, 5) (dual of [2404, 2392, 6]-code), using
- generalized (u, u+v)-construction [i] based on
- linear OA(251, 601, F25, 1) (dual of [601, 600, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(251, 601, F25, 1) (dual of [601, 600, 2]-code) (see above)
- linear OA(253, 601, F25, 2) (dual of [601, 598, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(253, 624, F25, 2) (dual of [624, 621, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(253, 624, F25, 2) (dual of [624, 621, 3]-code), using
- linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- linear OA(251, 601, F25, 1) (dual of [601, 600, 2]-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(2512, 2404, F25, 5) (dual of [2404, 2392, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2512, 2403, F25, 5) (dual of [2403, 2391, 6]-code), using
- net defined by OOA [i] based on linear OOA(2512, 1201, F25, 5, 5) (dual of [(1201, 5), 5993, 6]-NRT-code), using
- digital (40, 51, 1677720)-net over F25, using
- net defined by OOA [i] based on linear OOA(2551, 1677720, F25, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2551, 8388601, F25, 11) (dual of [8388601, 8388550, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2551, large, F25, 11) (dual of [large, large−51, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2551, large, F25, 11) (dual of [large, large−51, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2551, 8388601, F25, 11) (dual of [8388601, 8388550, 12]-code), using
- net defined by OOA [i] based on linear OOA(2551, 1677720, F25, 11, 11) (dual of [(1677720, 11), 18454869, 12]-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 (73, 84, 3357842)-net over F25 | [i] | (u, u+v)-Construction for Nets | |