Shift Register Sequences
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
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The binary linear feedback shift register sequences of degree n and maximum period p = 2n - 1 (the m-sequences) are useful in numerous applications because, although deterministic, they satisfy a number of interesting "randomness properties". An important open question is whether a binary sequence of period p = 2n - 1 with both the span-n property and the two-level correlation property must be an m-sequence. There is a direct correspondence between m-sequences of degree n and primitive polynomials of degree n over GF(2). Several conjectures are presented about primitive polynomials with a bounded number of terms.