A finite Gilbert-Varshamov bound for pure stabilizer (binary and nonbinary) quantum error correcting codes is presented in analogy to the GV bound for classical codes.Expand

Abstract To a regular hypergraph we attach an operator, called its adjacency matrix, and study the second largest eigenvalue as well as the overall distribution of the spectrum of this operator. Our… Expand

A linear error-block code is a natural generalization of the classical error-correcting code and has applications in experimental design, high-dimensional numerical integration and cryptography.Expand

In this paper, we will study the exponential sum SigmaxisinF<sub>q</sub> x(alphax(p<sup>k</sup>+1)/2+betax) that is related to the generalized Coulter-Matthews function x(pk+ 1)/2 with k/gcd.Expand

Abstract In this paper we determine all elliptic curves E n : y 2 = x 3 − n 2 x with the smallest 2-Selmer groups S n = Sel 2 ( E n ( Q ))={1} and S n ′= Sel 2 ( E n ′( Q ))={±1,± n }( E n ′: y 2 = x… Expand

In this paper we present a unified way to determine the values and their multiplicities of the exponential sums Sigma<sub>xisinF(q)</sub>zeta <sup>Tr(af(x)+bx)</sup>(a,bisinF< sub>q</sub>,q=p<sup>m</sup>,pges3) for all perfect nonlinear functions f which is a Dembowski-Ostrom polynomial.Expand

We prove that nonbinary quantum stabilizer codes with parameters [[n, k, d]]/sub p/ exist for all odd primes p by using graph machinery, given by Schlingemann and Werner.Expand