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Construction of Several Classes of Single-cycle Polynomials over Z/(pn) |
You Wei Qi Wen-feng |
Information Engineering University, Zhengzhou 450002, China |
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Abstract This paper studies single-cycle polynomials over the integer residue ring Z/(pn) with prime p≥5 and integer n≥2, and presents several classes of such single-cycle polynomials. As the research of single-cycle polynomials over Z/(pn) can be reduced to the case over Z/(p2), an exact characterization of single-cycle polynomials over Z/(5) is given in terms of their coefficients, and then a complete characterization of single-cycle polynomials of degree 6 over Z/(52) is given based on it. In addition, a partial construction of single-cycle polynomials of degree (p−1) over Z/(p2) is also proposed.
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Received: 09 June 2011
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Corresponding Authors:
You Wei
E-mail: youwei1102@163.com
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