منابع مشابه
Linear Complexity of the x2 Mod p Orbits
A lower bound for the linear complexity of sequences generated by the quadratic function x2 mod p is given. 1999 Published by Elsevier Science B.V. All rights reserved.
متن کاملDEGREE-k LINEAR RECURSIONS MOD(p) AND NUMBER FIELDS
Linear recursions of degree k are determined by evaluating the sequence of Generalized Fibonacci Polynomials, {Fk,n(t1, ..., tk)} (isobaric reflects of the complete symmetric polynomials) at the integer vectors (t1, ..., tk). If Fk,n(t1, ..., tk) = fn, then fn − k ∑ j=1 tjfn−j = 0, and {fn} is a linear recursion of degree k. On the one hand, the periodic properties of such sequences modulo a pr...
متن کاملRANK p − 1 MOD - p H - SPACES
Different constructions by Cooke, Harper and Zabrodsky and by Cohen and Neisendorfer produce torsion free finite p-local H-spaces of rank l < p−1. The first construction goes through when l = p− 1 and we show the second does as well. However, the space produced need not be an H-space. We give a criterion for when an H-space is obtained. In the special case of rank 2 mod-3 H-spaces, we also give...
متن کاملUniqueness of Optimal Mod 3 Circuits for Parity
In this paper, we prove that the quadratic polynomials modulo 3 with the largest correlation with parity are unique up to permutation of variables and constant factors. As a consequence of our result, we completely characterize the smallest MAJ◦ MOD3 ◦ AND2 circuits that compute parity, where a MAJ ◦MOD3 ◦ AND2 circuit is one that has a majority gate as output, a middle layer of MOD3 gates and ...
متن کاملUniqueness of Optimal Mod 3 Polynomials for Parity
In this paper, we completely characterize the quadratic polynomials modulo 3 with the largest (hence “optimal”) correlation with parity. This result is obtained by analysis of the exponential sum
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1986
ISSN: 0022-314X
DOI: 10.1016/0022-314x(86)90052-1