Information on Result #1191862
Digital (73, 88, 74900)-net over F8, using net defined by OOA based on linear OOA(888, 74900, F8, 15, 15) (dual of [(74900, 15), 1123412, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(888, 524301, F8, 15) (dual of [524301, 524213, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(888, 524304, F8, 15) (dual of [524304, 524216, 16]-code), using
- trace code [i] based on linear OA(6444, 262152, F64, 15) (dual of [262152, 262108, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(6443, 262145, F64, 15) (dual of [262145, 262102, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(6437, 262145, F64, 13) (dual of [262145, 262108, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- trace code [i] based on linear OA(6444, 262152, F64, 15) (dual of [262152, 262108, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(888, 524304, F8, 15) (dual of [524304, 524216, 16]-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 (74, 89, 74900)-net over F8 | [i] | Net Duplication | |