following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...

It is well known that a convolutional code is essentially a linear system defined over a finite field. In this paper we elaborate on this connection. We define a convolutional code as the dual of a complete linear behavior in the sense of Willems (1979). Using ideas from systems theory, we describe a set of generalized first-order descriptions for convolutional codes. As an application of these...

Most database systems translate a given query into an expression in a (physical) algebra, and then start evaluating this algebraic expression to produce the query result. The traditional way to execute these algebraic plans is the iterator model: Every physical algebraic operator conceptually produces a tuple stream from its input, and allows for iterating over this tuple stream. This is a very...

Space-time codes for a wide variety of channels have the property that the diversity of a pair of codeword matrices is measured by the vanishing or non-vanishing of polynomials in the entries of the matrices. We show that for every such channel: I) There is an appropriately-defined notion of approximation of space-time codes such that each code is arbitrarily well approximated by one whose alph...

With the knowledge of the syndromes Sa,b, 0 ≤ a, b ≤ q − 2, the exact error values cannot be determined by using the conventional (q − 1)2-point discrete Fourier transform in the decoding of a plane algebraic-geometric code over GF (q). In this letter, the inverse q-point 1-dimensional and q2-point 2dimensional affine Fourier transform over GF (q) are presented to be used to retrieve the actual...

In this paper, we introduce a lower bound for the generalized Hamming weights, which is applicable to arbitrary linear code, in terms of the notion of well-behaving. We also show that any [n, k] linear code C over a finite field F is the t-th rank MDS for t such that g(C) + 1 ≤ t ≤ k where g(C) is easily calculated from the basis of F so chosen that whose first n − k elements generate C⊥. Final...

Modelica is a new object-oriented multi-domain modeling language based on algebraic and differential equations. In this paper we present an environment that integrates different phases of the Modelica development lifecycle. This is achieved by using the Mathematica environment and its structured documents, “notebooks”. Simulation models are represented in the form of structured documents, which...

The latest version of the particle optics code COSY INFINITY is presented. Using Di!erential Algebraic (DA) methods, the code allows the computation of aberrations of arbitrary "eld arrangements to in principle unlimited order. Besides providing a general overview of the code, several recent techniques developed for speci"c applications are highlighted. These include new features for the direct...

For a linear code C of length n and dimension k, Wolf noticed that the trellis state complexity s(C) of C is upper bounded by w(C) := min(k, n− k). In this paper we point out some new lower bounds for s(C). In particular, if C is an Algebraic Geometric code, then s(C) ≥ w(C) − (g − a), where g is the genus of the underlying curve and a is the abundance of the code.

A locally recoverable code is a code over a finite alphabet such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. Building on work of Barg, Tamo, and Vlăduţ, we present several constructions of locally recoverable codes from algebraic curves and surfaces.