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Analysis and synthesis of polynomials and sequences over GF(2)

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1 Author(s)

The analysis and synthesis of polynomials and sequences over GF(2) has received considerable attention in recent years with the increasing use of PN sequences. In this paper a new approach to the problem is presented in which the polynomial coefficients and the sequence digits are derived in terms of the values assumed by a special class of polynomials, called "cyclonomials," at an arbitrary primitive element of GF(2^n) . For each value of n the cyclonomials are determined by the partition of the set { 0,1,2, \cdots ,2^n - 2 } into cyclotomic cosets. A method of deriving all primitive polynomials of degree n from a given one of the same degree is described. A short outline of an approach to the more difficult task of synthesizing an initial primitive polynomial is also presented.

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Information Theory, IEEE Transactions on  (Volume:17 ,  Issue: 3 )