Interleaved Reed–Solomon codes are applied in numerous data processing, data transmission, and data storage systems. They are generated by interleaving several codewords of ordinary Reed–Solomon codes. Usually, these codewords are decoded independently by classical algebraic decoding methods. However, by collaborative algebraic decoding approaches, such interleaved schemes allow the correction ...

The theory of error-correcting codes derived from curves in an algebraic geometry was initiated by the work of Goppa as generalizations of Bose-Chaudhuri-Hocquenghem (BCH), Reed–Solomon (RS), and Goppa codes. The development of the theory has received intense consideration since that time and the purpose of the paper is to review this work. Elements of the theory of algebraic curves, at a level...

10]. Abuse [75]. Abuse-Free [75]. Access [64]. Active [32]. Addition [110]. Adolescence [1]. Age [61]. Agent [125]. Algebraic [63]. Algebraic-Code [63]. Algorithm [88]. Algorithms [13]. Alive [6]. Almost [60]. Alternative [19]. and/or [44]. Antique [94]. Any [10]. Application [43]. Applications [17]. Architecture [106]. Argued [21]. Atkin [59]. Attack [56]. Attacks [32]. Authentication [2]. Aut...

The polyhedral model is a powerful framework for automatic optimization and parallelization. It is based on an algebraic representation of programs, allowing to construct and search for complex sequences of optimizations. This model is now mature and reaches production compilers. The main limitation of the polyhedral model is known to be its restriction to statically predictable, loop-based pro...

We construct a new list-decodable family of asymptotically good algebraic-geometric (AG) codes over fixed alphabets. The function fields underlying these codes are constructed using class field theory, specifically Drinfeld modules of rank 1, and designed to have an automorphism of large order that is used to “fold” the AG code. This generalizes earlier work by the first author on folded AG cod...

We propose a special relation algebraic model as semantics for lazy functional logic languages. The resulting semantics provides several interesting advantages over former approaches for this class of languages. For once, the equational reasoning supported by an algebraic approach implies a great increase in the economy and readability of proofs. Second, the richly developed field of relation a...

Algebraic-geometric codes can be constructed by evaluating a certain set of functions on a set of distinct rational points of an algebraic curve. The set of functions that are evaluated is the linear space of a given divisor or, equivalently, the set of section of a given line bundle. Using arbitrary rank vector bundles on algebraic curves, we propose a natural generalization of the above const...

This paper presents the performance of carrier Frequency offset estimation algorithm for golden encoded MIMO OFDM system. Basically Algebraic Space Time Code (ASTC) has three major encoding methods they are Golden, TAST and DAST encoding. But Golden encoder provides an efficient performance while compared with the TAST and DAST. Carrier frequency offset estimated for Golden code multiple input ...

A. Silverberg (IEEE Trans. Inform. Theory 49, 2003) proposed a question on the equivalence of identifiable parent property and traceability property for Reed-Solomon code family. Earlier studies on Silverberg’s problem motivate us to think of the stronger version of the question on equivalence of separation and traceability properties. Both, however, still remain open. In this article, we integ...

Abstract State Machines (ASMs) have been widely used to specify software and hardware systems. Only a few of these specifications are executable, although there are several interpreters and some compilers. This paper introduces a compilation scheme to transform an ASM specification in the syntax of the ASM-Workbench into C++. In particular, we transform algebraic types, pattern matching, functi...