相关论文: Minimum distance of Hermitian two-point codes

The computation of the distance between any two points of the Sierpinski Gasket with respect to the intrinsic metric has already been investigated by several authors. In the literature there is not an explicit formula using the code space…

In this paper we present several classes of asymptotically good concatenated quantum codes and derive lower bounds on the minimum distance and rate of the codes. We compare these bounds with the best-known bound of…

Finding an exact maximum distance of two points in the given set is a fundamental computational problem which is solved in many applications. This paper presents a fast, simple to implement and robust algorithm for finding this maximum…

In the following paper we continue the work of Bimonte-Lizzi-Sparano on distances on a one dimensional lattice. We succeed in proving analytically the exact formulae for such distances. We find that the distance to an even point on the…

We present a linked-cluster technique for calculating the distance of a quantum LDPC code. It offers an advantage over existing deterministic techniques for codes with small relative distances (which includes all known families of quantum…

Bicyclic codes are a generalization of the one dimensional (1D) cyclic codes to two dimensions (2D). Similar to the 1D case, in some cases, 2D cyclic codes can also be constructed to guarantee a specified minimum distance. Many aspects of…

We give an elementary proof of the group law for elliptic curves using explicit formulas.

A partial formula is provided to calculate the smallest number of vertices possible in a quadrangulation on the closed orientable 2-manifold of given genus. This extends the previously known partial formula due to N. Hartsfield and G.…

For a given curve X and divisor class C, we give lower bounds on the degree of a divisor A such that A and A-C belong to specified semigroups of divisors. For suitable choices of the semigroups we obtain (1) lower bounds for the size of a…

We introduce and study the minimum distance function of a graded ideal in a polynomial ring with coefficients in a field, and show that it generalizes the minimum distance of projective Reed-Muller-type codes over finite fields. This gives…

Subfield subcodes of algebraic-geometric codes are good candidates for the use in post-quantum cryptosystems, provided their true parameters such as dimension and minimum distance can be determined. In this paper we present new values of…

Two generalizations of the Hartmann--Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed. The first one is proven by embedding the given cyclic code into a cyclic product code. Furthermore, we show that unique…

Let $\Gamma$ be a geometrically-finite Fuchsian group acting on the upper half plane $\hh.$ Let $\E$ denote the set of elliptic fixed points of $\Gamma$ in $\hh.$ We give a lower bound on the minimal hyperbolic distance between points in…

For $k \ge 2$ and a positive integer $d_0$, we show that if there exists no quaternary Hermitian linear complementary dual $[n,k,d]$ code with $d \ge d_0$ and Hermitian dual distance greater than or equal to $2$, then there exists no…

We discuss a non-computational elementary approach to a well-known criterion of divisibility by 2 in the group of rational points on an elliptic curve.

A criterion for the existence of a plane model of an algebraic curve such that the Galois closures of projections from two points are the same is presented. As an application, it is proved that the Hermitian curve in positive characteristic…

We obtain lower bound for the maximum distance between any three distinct points in an affine lattice which are close to a helix with small curvature and torsion.

We propose a novel iterative process to establish the minimum separation between two ellipsoids. The method maintains one point on each surface and updates their locations in the theta-phi parametric space. The tension along the connecting…

We prove lower bounds for the minimum distance of algebraic geometry codes over surfaces whose canonical divisor is either nef or anti-strictly nef and over surfaces without irreducible curves of small genus. We sharpen these lower bounds…

In this paper, we propose a sufficient condition for a family of 2-generator self-orthogonal quasi-cyclic codes with respect to Hermitian inner product. Supported in the Hermitian construction, we show algebraic constructions of good…