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Simple Constructions of Almost k‐wise Independent Random Variables
Abstract
We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 +o(1)) (log log n+k/2 + log k+ log 1/ϵ), where ϵ is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as ϵ < 1/(k log n)). An additional advantage of our constructions is their simplicity.
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Cited by
Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals
Tropp, J. A., Laska, J. N., Duarte, M. F., Romberg, J. K., & Baraniuk, R. G. (2010) · IEEE Transactions on Information Theory · doi:10.1109/tit.2009.2034811 · Cited by 1,089
Property testing and its connection to learning and approximation
Goldreich, O., Goldwasser, S., & Ron, D. (1998) · Journal of the ACM · doi:10.1145/285055.285060 · Cited by 1,020
Self-citationCheraghchi, M., Gabrys, R., Milenkovic, O., & Ribeiro, J. (2020) · IEEE Transactions on Information Theory · doi:10.1109/tit.2020.2996377 · Cited by 90
Metadata
- Authors
- Alon, N., Goldreich, O., Håstad, J., & Peralta, R.
- Venue
- Random Structures & Algorithms
- Publisher
- Wiley
- Published
- 1992-01
- Volume
- 3
- Issue
- 3
- Pages
- 289-304
- ISSN
- 1042-9832 (ISSN-L)
- 1098-2418
- OpenAlex
- W2163137752
- Cited by
- 556
- References
- 0
- FWCI
- 27.28
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Simple Constructions of Almost k‐wise Independent Random Variables. https://app.cochat.ai/papers/10.1002/rsa.3240030308
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- Alon, N., Goldreich, O., Håstad, J., & Peralta, R. (1992). Simple Constructions of Almost k‐wise Independent Random Variables. Random Structures & Algorithms. https://doi.org/10.1002/rsa.3240030308
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