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.
ZHAO Yan
,
LIN Dong-Dai
. Nonsingular circulant matrices over finite fields[J]. Journal of University of Chinese Academy of Sciences, 2012
, (6)
: 805
-814
.
DOI: 10.7523/j.issn.2095-6134.2012.6.013
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