Algorithms for Finding Inverse of Two Patterned Matrices over Zp

Abstract

Circulant matrix families have become an important tool in network engineering. In this paper, two new patterned matrices over ${\mathbb{Z}}_p$ which include row skew first-plus-last right circulant matrix and row first-plus-last left circulant matrix are presented. Their basic properties are discussed. Based on Newton-Hensel lifting and Chinese remaindering, two different algorithms are obtained. Moreover, the cost in terms of bit operations for each algorithm is given.