We present a complete, certificate-based decision procedure for first-order univariate polynomial problems in Isabelle [17]. It is built around an executable function to decide the sign of a univariate polynomial at a real algebraic point. The procedure relies on no trusted code except for Isabelle’s kernel and code generation. This work is the first step towards integrating the MetiTarski theo...

Given a suitable extension $ F'/F of algebraic function fields over finite field \mathbb{F}_q $, we introduce the conorm code \operatorname{Con}_{F'/F}( \mathcal{C}) defined F' which is constructed from an geometry \mathcal{C} F $. We study parameters in terms ramification behavior places used to define and genus In case unramified extensions prove that \mathcal{C})^\perp = \mathcal{C}^\perp) w...

In this paper we present a new family of fullrate space–time block codes for 4 × 2 MIMO. We show how, by combining algebraic and quasi-orthogonal properties of the code, reduced-complexity maximum-likelihood decoding is made possible. In particular, the sphere decoder search can be reduced from a 16to a 12-dimensional space. Within this family, we found a code that outperforms all previously pr...

We show that every self-orthogonal code over $\mathbb F_q$ of length $n$ can be extended to a self-dual code, if there exists self-dual codes of length $n$. Using a family of Galois towers of algebraic function fields we show that over any nonprime field $\mathbb F_q$, with $q\geq 64$, except possibly $q=125$, there are self-dual codes better than the asymptotic Gilbert--Varshamov bound.

The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a noisy quantum channel so as to make it intelligible to engineers. An illustrative example is presented of a naïve perfect quantum code (Hamming-like code) with five-qubits for transmitting a single qubit of information....

We provide a simple, closed-form upper bound for the classical problem of worst case list-size of a general q-ary block code. This new bound improves upon the best known general bound when the alphabet of the code is large. We also show that with parameters of Reed-Solomon codes this bound is very close to the algebraic bound derived using the constructions of the Guruswami-Sudan decoder.

In this paper we discuss an upper bound on the free distance for a rate k / n convolutional code with complexity b . Using th i s bound we in t roduce the notion of a MDS convolutional code. We also give an algebraic way of cons t ruc t ing b inary codes of rate 1/2 and large complexity. The obta ined distances compare favorably to the distances found by computer searches and probabilistic meth...

In this paper we discuss the problem of collusion secure fingerprinting. In the first part of our contribution we prove the existence of equidistant codes that can be used as fingerprinting codes. Then we show that by giving algebraic structure to the equidistant code, the tracing process can be accomplished by passing a modified version of the Viterbi algorithm through the trellis representing...

Our purpose is to present some computations and estimates for the minimum distance of some families of evaluation codes. We introduce the Feng-Rao distance of an algebraic-geometry code and its extension to codes from order domains. Finally we give an algorithm to compute the Feng-Rao distance of a code from an order domain and we show its implementation in the computer algebra system SINGULAR.

        In the present study, the effect of random distribution of reactants and products on laminar, 2D and steady-state flame propagation in aluminium particles has been investigated. The equations are solved only for lean mixture. The flame structure is assumed to consist of a preheat zone, a reaction zone and a post flame zone. It is presumed that in the preheat zone particles are heated an...