A Simple Construction of Almost k-wise Independent Random Variables
نویسندگان
چکیده
We present a simple construction of a small probability space 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 O(log log n + k + log ~), where e is the statistical difference between of 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. An additional advantage of our construction is its simplicity. Loosely speaking, the sample space consists of the set of sequences obtained from a linear feedback shift register on various short start and feedback sequences. ·Supported by grant No. 86-00301 from the United States Israel Binational Science Foundation (BSF), Jerusalem, Israel.
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