Linear recurring sequences over Galois rings
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Linear recurrences of maximal period over a Galois ring and over a residue class ring modulo p are studied. For any such recurrence, the coordinate sequences (in p-adic and some other expansions) are considered as linear recurring sequences over a finite field. Upper and lower bounds for the ranks (linear complexities) of these coordinate sequences are obtained. The results are based on using the properties of Galois rings and the trace-function on such rings.
KeywordsLower Bound Mathematical Logic Finite Field Linear Complexity Residue Class
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- 1.A. S. Kuzmin and A. A. Nechaev, “Linear recurring sequences over Galois rings,” inInternational Conference on Algebra, Barnaul (1991).Google Scholar
- 2.A. A. Nechaev, “Finite rings of principal ideals,”Mat. Sb.,91, No. 3, 350–366 (1973).Google Scholar
- 3.R. Radghavendran, “Finite associative rings,”Comp. Math.,21, 195–229 (1969).Google Scholar
- 4.B. R. McDonald,Finite Rings with Identity, Dekker, New York (1974).Google Scholar
- 5.A. A. Nechaev, “Cyclic types of linear substitutions over finite commutative local rings,”Mat. Sb.,184, No. 3, 21–56 (1993).Google Scholar
- 6.A. A. Nechaev, “Kerdock's code in cyclic form,”Diskr. Mat.,1, No. 4, 123–139 (1989).Google Scholar
- 7.V. N. Sachkov,Combinatorial Methods in Discrete Mathematics [in Russian], Nauka, Moscow (1977).Google Scholar
- 8.Z. Dai and D. Gollmann, “Lower bounds for the linear complexity of sequences over residue rings,” inEuroCrypt'90, Aarhus (1990), pp. 175–179.Google Scholar
- 9.A. A. Nechaev, “Trace-function in a Galois ring and noise-stable codes,” inV All-Union Symposium on Theory of Rings, Algebras, and Modules, Novosibirsk (1982).Google Scholar
- 10.N. Zierler and W. Mills, “Products of linear recurring sequences,”J. Alg.,27, 147–157 (1973).Google Scholar
- 11.E. R. Berlekamp,Algebraic Coding Theory, McGraw-Hill, New York (1968).Google Scholar