Related papers: Algebra in Algorithmic Coding Theory
We revisit a concept that has been central in some early stages of computer science, that of structured programming: a set of rules that an algorithm must follow in order to acquire a structure that is desirable in many aspects. While much…
We study Algebraic Geometry codes producing quantum error-correcting codes by the CSS construction. We pay particular attention to the family of Castle codes. We show that many of the examples known in the literature in fact belong to this…
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
We propose an approach to image processing related to algebraic operators acting in the space of images. In view of the interest in the applications in optics and computer science, mathematical aspects of the paper have been simplified as…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we…
Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines. With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial…
Despite ongoing calls for inclusive and culturally responsive pedagogy in computing education, the teaching of algorithms remains largely decontextualized. Foundational computer science courses often present algorithmic thinking as purely…
Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…
In this pages I give an overview of the relationship between Model Theory, Arithmetic and Algebraic Geometry. The topics will be the basic ones in the area, so this is just an invitation, in the presentation of topics I mainly follow the…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
This thesis is a study of quantum error-correction codes from an algebraic perspective. We concern ourselves not only with quantum codes but also protocols to perform logical quantum computation using such codes. We derive new methods of…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…
Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area…
Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker,…
This paper introduces a new inequality in algorithmic information theory that can be seen as an extended coding theorem. This inequality has applications in new bounds between quantum complexity measures.
Qualitative data analysis provides insight into the underlying perceptions and experiences within unstructured data. However, the time-consuming nature of the coding process, especially for larger datasets, calls for innovative approaches,…
We present a general construction of the derived category of an algebra over an operad and establish its invariance properties. A central role is played by the enveloping operad of an algebra over an operad.
In the framework quotient algebra partition, a general methodology is introduced to construct fault tolerant encodes for an arbitrary action in an error-correcting code.
In a previous paper, a process algebra based on ACP (Algebra of Communicating Processes) was proposed in which processes involving data can be handled by means of features originating from imperative programming. In this paper, an extension…
The deletion channel is known to be a notoriously diffcult channel to design error-correction codes for. In spite of this difficulty, there are some beautiful code constructions which give some intuition about the channel and about what…