Information on Result #1188782
Digital (59, 72, 13023)-net over F5, using net defined by OOA based on linear OOA(572, 13023, F5, 13, 13) (dual of [(13023, 13), 169227, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(572, 78139, F5, 13) (dual of [78139, 78067, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(572, 78141, F5, 13) (dual of [78141, 78069, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(571, 78126, F5, 13) (dual of [78126, 78055, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(557, 78126, F5, 11) (dual of [78126, 78069, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(51, 15, F5, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- discarding factors / shortening the dual code based on linear OA(572, 78141, F5, 13) (dual of [78141, 78069, 14]-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 (60, 73, 13023)-net over F5 | [i] | Net Duplication | |
| 2 | Digital (61, 74, 13023)-net over F5 | [i] | ||