Information on Result #1749413
Digital (58, 71, 688)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(271, 688, F2, 3, 13) (dual of [(688, 3), 1993, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(271, 2064, F2, 13) (dual of [2064, 1993, 14]-code), using
- 2 times code embedding in larger space [i] based on linear OA(269, 2062, F2, 13) (dual of [2062, 1993, 14]-code), using
- adding a parity check bit [i] based on linear OA(268, 2061, F2, 12) (dual of [2061, 1993, 13]-code), using
- construction X4 applied to C([0,12]) ⊂ C([1,10]) [i] based on
- linear OA(267, 2047, F2, 13) (dual of [2047, 1980, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(255, 2047, F2, 10) (dual of [2047, 1992, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(213, 14, F2, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,2)), using
- dual of repetition code with length 14 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to C([0,12]) ⊂ C([1,10]) [i] based on
- adding a parity check bit [i] based on linear OA(268, 2061, F2, 12) (dual of [2061, 1993, 13]-code), using
- 2 times code embedding in larger space [i] based on linear OA(269, 2062, F2, 13) (dual of [2062, 1993, 14]-code), using
Mode: 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 (59, 72, 688)-net over F2 | [i] | Net Duplication | |