Systematic Authentication Codes Research Articles

Complete Weight Enumerator for a Class of Linear Codes from Defining Sets and Their Applications

Recently, linear codes over finite fields with a few weights have been extensively studied due to their applications in secret sharing schemes, authentication codes, constant composition codes. In this paper, for an odd prime p, the complete weight enumerator of a class of p-ary linear codes based on defining sets are determined. Furthermore, from the explicit complete weight enumerator of linear codes, a new class of optimal constant composition codes and several classes of asymptotically optimal systematic authentication codes are obtained.

An Authentication Code over Galois Rings with Optimal Impersonation and Substitution Probabilities

Two new systematic authentication codes based on the Gray map over a Galois ring are introduced. The first introduced code attains optimal impersonation and substitution probabilities. The second code improves space sizes, but it does not attain optimal probabilities. Additionally, it is conditioned to the existence of a special class of bent maps on Galois rings.

New constructions of systematic authentication codes from three classes of cyclic codes

Recently, several classes of cyclic codes with three nonzero weights were constructed. With the generic construction presented by C. Ding, T. Helleseth, T. Klove and X. Wang, we present new systematic authentication codes based on these cyclic codes. In this paper, we study three special classes of cyclic codes and their authentication codes. With the help of exponential sums, we calculate the maximum success probabilities of the impersonation and substitution attacks on the authentication codes. Our results show that these new authentication codes are better than some of the authentication codes in the literature. As a byproduct, the number of times that each element occurs as the coordinates in the codewords of the cyclic codes is settled, which is a difficult problem in general.

Complete weight enumerators of three classes of linear codes

In recent years, a great deal of effort has been devoted to the study of linear codes with few weights, since they have applications in secret sharing, authentication codes, association schemes and some other fields. In this paper, we propose three classes of linear codes by using proper defining sets and investigate their complete weight enumerators. As applications, these linear codes are employed to construct secret sharing schemes with access structures and systematic authentication codes. Moreover, we obtain three classes of asymptotically optimal systematic authentication codes.

Complete weight enumerators of a class of linear codes with two weights

In this paper, a class of p-ary linear codes with two weights is constructed by using the properties of cyclotomic classes of Fp2∗. The complete weight enumerators of these linear codes are also determined. In some cases, they are optimal and can be employed to obtain secret sharing schemes with interesting access structures and asymptotically optimal systematic authentication codes.

Complete weight enumerators of some linear codes and their applications

Recently, linear codes constructed from defining sets have been extensively studied. It was shown that the linear codes may have a few nonzero weights or be optimal if the defining sets are well chosen. The weight enumerators of these linear codes were also presented. In this paper, we investigate the complete weight enumerators of some linear codes constructed from the defining sets. As applications, we employ the explicit complete weight enumerators of the linear codes to construct constant composition codes and systematic authentication codes. A new class of optimal constant composition codes and three classes of asymptotically optimal systematic authentication codes are presented.

Systematic Authentication Codes Based on a Class of Bent Functions and the Gray Map on a Galois Ring

We use a class of bent functions on a Galois ring of characteristic $p^2$ and the Gray map on this ring to construct new classes of systematic authentication codes.

Bent functions on a Galois ring and systematic authentication codes

A class of bent functions on a Galois ring is introduced and based on these functions systematic authentication codes are presented. These codes generalize those appearing in [4] for finite fields.

Systematic authentication codes using additive polynomials

Using additive polynomials related to some curves over finite fields, we construct two families of systematic authentication codes. We use tight bounds for the number of rational points of these curves in estimating the probabilities of the systematic authentication codes. We compare their parameters with some existing codes in the literature. We observe that the parameters are better than the existing ones in some cases.

Some constructions of systematic authentication codes using galois rings

For q = p m and m ? 1, we construct systematic authentication codes over finite field $$\mathbb{F}_{q}$$ using Galois rings. We give corrections of the construction of [2]. We generalize corresponding systematic authentication codes of [6] in various ways.

Systematic Authentication Codes From Highly Nonlinear Functions

Recently, highly nonlinear functions have been successfully employed to construct authentication codes with and without secrecy. In this paper, we construct four classes of systematic authentication codes from perfect nonlinear functions and almost-perfect nonlinear functions. The systematic authentication codes presented in this paper are either better than existing codes or as good as the best codes known.

Difference packing arrays and systematic authentication codes

In this paper, a type of combinatorial design (called difference packing array) is proposed and used to give a construction of systematic authentication codes. Taking advantage of this construction, some new series of systematic authentication codes are obtainable in terms of existing difference packing arrays.

Constructions of difference covering arrays

A difference covering array with parameters k, n and q, or a DCA( k, n; q) for short, over a group ( G,•) of order q is defined to be a k× n array ( a ij ) with entries a ij (0⩽i⩽k−1,0⩽ j⩽n−1) from G such that, for any two distinct rows t and h (0⩽ t< h⩽ k−1), every element of G occurs in the difference list {d hj•d tj −1 : j=0,1,…,n−1} at least once. It is clear that n⩾ q in a DCA( k, n; q). The equality holds if and only if a ( q, k,1) difference matrix exists. It is well known that a ( q, k,1) difference matrix does not exist, whenever q≡2 ( mod 4) and k⩾3. Thus, we have n⩾ q+1 for these values of k and q. In this article, several constructive techniques for DCAs are presented, and used to solve completely the existence problem for a DCA(4, q+1; q) with q≡2 ( mod 4) . This complements the study for difference matrices in literature. The result is also useful in encoding systematic authentication codes, as well as in software testing and data compression problems.