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We provide an introductory overview of how exponential sums, and bounds for them, have been exploited by coding theorists and communications engineers.
Recent years have seen numerous examples where designs play an important role in the study of such topics in cryptography as secrecy and authentication codes, secret sharing schemes, correlation-immune and resilient functions. In this paper we give applications of some methods and results from the design theory, especially bounding the optimal size of the designs and codes, to cryptography. We give...
A good design of a Boolean function used in a stream cipher requires that the function satisfies certain criteria in order to resist different attacks. In this paper we study the tradeoff between two such criteria, the nonlinearity and the resiliency. The results are twofold. Firstly, we establish the maximum nonlinearity for a fixed resiliency in certain cases. Secondly, we present a simple search...
This paper shows the connection between the combinatorial structure of two dimensional metrics over finite fields ( Shortly, Mannheim and Hexagonal metrics) and some group actions defined over them. We follow the well known approach of P. Delsarte [9] to this problem through the construction of association schemes. Association schemes based on this distances are the basic tools we propose to deal...
A new, systematic method of generating orthogonal sets of sequences with good correlation properties is described. An orthogonal set is defined as a collection of n sequences, of length n chips, that are mutually orthogonal. Although there are many possible combinations of sequences forming orthogonal sets of a specified length, few have been identified with a structured method of generation such...
Self-dual codes and orthogonal designs have been studied for a long time as separate research areas. In the present paper we show a strong relationship between them. The structure of orthogonal designs is such as to allow us a much faster and more systematic search for self-dual codes over GF(5). Using our method we constructed the following linear self-dual codes over GF(5):(i) [4,2,2], (ii)...
Determining the weight of Boolean functions is of exponential complexity. By using combinatorial results, it is proved that from their algebraic normal form (ANF), it is possible to have polynomial time results on the weight, for some classes of functions. As a result, the structure of the majority functions MAJ2q-1 is given.
This paper provides a brief insight in satellite communication systems from the perspective of coding applications. CDMA based systems for use in Low Earth Orbit (LEO) satellite systems is the focus of the paper. The code-division-multiple-access (CDMA) format is emerging as a dominant air interface technology for cellular, personal-communications-services (PCS) as well as satellite installations...
We have proposed a novel scheme based on arithmetic coding, an optimal data compression algorithm in the sense of shortest length coding. Our scheme can provide encryption, data compression, and error detection, all together in a one-pass operation. The key size used is 248 bits. The scheme can resist existing attacks on arithmetic coding encryption algorithms. A general approach to attacking this...
This paper explores the application of a combined error resilient coding scheme to image transmission over time-varying noisy channels. To improve performance at low signal-to-noise ratios, turbo coding is incorporated into the system. Demonstrated through simulations, this novel combination of source and channel coding is shown to correct and restrict errors incurred during transmission over Additive...
A biometric identification system was recently developed and analyzed as a secure mechanism for user authentication. The system provided for the confidentiality, without the use of cryptographic encryption, of the user’s biometric information stored in public verification templates. Here we demonstrate that the use of majority decoding can enhance the prior techniques in several ways. One enhancement...
In this paper, we propose an encoding scheme which gives two levels of access to a broadcast encrypted signal. Watermarking-type techniques based on direct-sequence spread spectrum communications are implemented to add specific information to the signal within the bandwidth allocated for broadcasting. This is beneficial to both the service providers and all subscribers in the network since the information...
This paper investigates a photo-signature approach to protecting personal identification documents such as passports. The approach is based on that described in a recent publication by O’Gorman and Rabinovich [1] which uses encoded data derived from comparisons of image sub-blocks across the photograph of the document. The encoded data is generated and stored at the time of document creation, and...
When decoding a threshold phenomenon is often observed: decoding deteriorates very suddenly around some critical value of the channel parameter. Threshold behaviour has been studied in many situations outside coding theory and a number of tools have been developped. One of those turns out to be particularly relevant to coding, namely the derivation of isoperimetric inequalities for product measures...
A rectangular code is a code for which there exists an unique minimal trellis. Such a code can be considered to be an algebraically closed set under the rectangular complement operation. The notions of rectangular closure and basis were already defined. In this paper we represent a method to construct a rectangular basis of a linear code from a given linear basis.
The motivation for this paper is to report on concepts and results arising from the continuation of a recent study [1] of graph decoding techniques for block error-control (detection and correction) codes. The representation of codes by means of graphs, and the corresponding graph-based decoding algorithms, are described briefly. Results on the performance of graph decoding methods for block codes...
A new catastrophicity test for convolutional encoders whose rate and generator polynomials vary with time is presented. Based on this test computationally efficient algorithm to determine whether or not a time-varying convolutional encoder is catastrophic is derived. This algorithm is shown to be simpler than the catastrophicity test proposed by Balakirsky [1]. Furthermore, the algorithm can easily...
We present a soft-decision decoding method for Reed-Solomon codes (RS codes) using both cyclic and squaring permutations. These permutations are used to provide a convenient sequence which is predicted to have relatively low complex error pattern with respect to a modified Fano sequential algorithm[1]. In order to preserve bit-level soft-decision values, each sequence of those permutation groups must...
Let R be a commutative ring e.g. the domain of p-adic integers or a Galois ring. We define alternant codes over R, which includes BCH and Reed-Solomon codes. We also define a corresponding key equation and concentrate on decoding alternant codes when R is a domain or a local ring. Our approach is based on minimal realization (MR) of a finite sequence [4,5], which is related to rational approximation...
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