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Inversion of two level circulant matrices over Z_p

Accettella, Carlo J. and Del Corso, Gianna M. and Manzini, Giovanni (2001) Inversion of two level circulant matrices over Z_p. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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    We consider the problem of inverting block circulant with circulant blocks BCCB matrices with entries over the field Z_p. This problem arises in the study of of two-dimensional linear cellular automata. Since the standard reduction to diagonal form by means of FFT has some drawbacks when working over Z_p, we solve this problem by transforming it into the equivalent problem of inverting a circulant matrix with entries over a suitable ring R. We show that a BCCB matrix of size mn can be inverted in O(m n c(m,n)) operations in Z_p, where c is a low degree polynomial in log m and log n.

    Item Type: Book
    Uncontrolled Keywords: Multilevel Circulant matrices, inversion over rings, Laurent series
    Subjects: Area01 - Scienze matematiche e informatiche > INF/01 - Informatica
    Divisions: Dipartimenti (until 2012) > DIPARTIMENTO DI INFORMATICA
    Depositing User: dott.ssa Sandra Faita
    Date Deposited: 22 Dec 2014 14:24
    Last Modified: 22 Dec 2014 14:24
    URI: http://eprints.adm.unipi.it/id/eprint/2062

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