Information on Result #1201248
Digital (17, 30, 685)-net over F64, using net defined by OOA based on linear OOA(6430, 685, F64, 13, 13) (dual of [(685, 13), 8875, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(6430, 4111, F64, 13) (dual of [4111, 4081, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(6430, 4114, F64, 13) (dual of [4114, 4084, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,3]) [i] based on
- linear OA(6425, 4097, F64, 13) (dual of [4097, 4072, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(6413, 4097, F64, 7) (dual of [4097, 4084, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(645, 17, F64, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- construction X applied to C([0,6]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(6430, 4114, F64, 13) (dual of [4114, 4084, 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 | (23, 36, 685)-net in base 32 | [i] | Base Change | |