The Characterisic Ideal Of Sequenccs And The Compression Mappings On Primitive Sequences Over Galois Rings

Let s be a linear recurring sequence over the residue ring ZI(pd) with prime p; and I(S,pd) be the ideal of all annihilating polynomials of the sequence s, which we called it as the Characteristic Ideal of the sequence s over Z/(pd). In this paper, with considering the Classic Generating Elements of the ideal of Z/(pd) [x], we construct an effective bridge between ideal and the linear recurring sequence over ZI(pd), and attain the exact condition that an ideal I of ZICpd) [x] is the Characteristic Ideal of some linear recurring sequence over Z/Cv4). All the same results over Galois rings are natural. Let Q be the Teichmuller representative set of Galois ring GR(2d,r), then for each sequence a over GR(2d,r), there exists a unique level decomposition a=a0+a1+... +adl.2dl, where a1 is a sequence over Q and can be regarded as a sequence over the finite field F2r naturally. Let fix) be a strongly primitive polynomial over GR(2d,r), G(f(x)) the set of sequences generated byf(x) over GR(2d,r) and tl(xo,XI,...,xd2) a polynomial of d variables over F2r. Set P(xo,XI,...,Xd1) =xdI+r(XO,xl ,...,xd2), then the compression mappingis injectiveness, that is, a=b if and only if p(ao,a,...,adI) = p(bo,bl,...,bdI) for a, beG(f(x)).