arXiv subjects

Mihai Caragiu

Publications and source records attributed to Mihai Caragiu.

4 recordsLinked to original sources

arXiv2019

A linear complexity analysis of quadratic residues and primitive roots spacings

We investigate the linear complexities of the periodic 0-1 infinite sequences in which the periods are the sequence of the parities of the spacings between quadratic residues modulo a prime p, and the sequence of the parities of the spacings between primitive roots modulo p, respectively. In either case, the Berlekamp-Massey algorithm running on MAPLE computer algebra software shows very good to perfect linear complexities.

cs.IT↗

arXiv2006

Fibonacci-Lucas densities

Both Fibonacci and Lucas numbers can be described combinatorially in terms of 0-1 strings without consecutive ones. In the present article we explore the occupation numbers as well as the correlations between various positions in the corresponding configurations.

math.GM↗

arXiv2005

Codekets

To every binary linear [n,k]-code C we associate a quantum state ("codeket") belonging to the n-th tensor power of the 2-dimensional complex Hilbert space associated to the spin 1/2 particle. We completely characterize the expectation values of the products of x-, y- or z- spins measured in the state we define, for each of the particles in a chosen subset. This establishes an interesting relationship with the dual code. We also address the case of nonlinear codes, and derive both a bound satisfied by the expectations of spin products, as well as a nice algebraic identity.

quant-ph↗

arXiv2005

An intermediate value theorem for sequences with terms in a finite set

We prove an intermediate value theorem of an arithmetical flavor, involving the consecutive averages of sequences with terms in a given finite set A. For every such set we completely characterize the numbers x ("intermediate values") with the property that the consecutive averages of every sequence with terms in A cannot increase from a value less than x to a value greater than x without taking the value x somewhere in between.

math.GM↗