Nonsingular circulant matrices over finite fields

doi:10.7523/j.issn.2095-6134.2012.6.013

›› 2012, Vol. ›› Issue (6): 805-814.DOI: 10.7523/j.issn.2095-6134.2012.6.013

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Nonsingular circulant matrices over finite fields

ZHAO Yan^1,2, LIN Dong-Dai¹

1. Institute of Software, Chinese Academy of Sciences, Beijing 100190, China;
2. Graduate University, Chinese Academy of Sciences, Beijing 100190, China

Received:2011-03-29 Revised:2011-05-05 Online:2012-11-15

Abstract

Abstract: Study on the number of nonsingular circulant matrices over finite fields is significant in both maticx theory and practice. We characterize the properties of circulant matrices over finite fields and find two different ways to solve the problem. Finally, we give the formula to figure out the number of the nonsingular circulant matrices over finite fields in all circumstances and analyze some applications of circulant matrices in MPKC.

Key words: circulant matrices, nonsingularity, finite fields, cryptography

CLC Number:

TN918.1

ZHAO Yan, LIN Dong-Dai. Nonsingular circulant matrices over finite fields[J]. , 2012, (6): 805-814.

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Nonsingular circulant matrices over finite fields

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