Theses

1. Krull Dimension and Classical Krull Dimension for Modules, Nahid Ghafourian-Jazi.

    Abstract: Using the concept of prime submodule defined by Raggi, for an R-module M, we define the concept of classical Krull dimension relative to a hereditary torsion theory. Some interesting results on the defined dimension are obtained.

2. Prime Elements in Partially Ordered Groupoids and Applications in Module Theory, Mahnaz Rajabpour.

    Abstract: Primeness on modules is defined by prime elements in a suitable partially ordered groupoid. We revise the concept of prime modules in this
sense. In particular we are interested in representing weakly compressible modules as a subdirect product of “prime” modules in a suitable sense. It turns out that any weakly compressible module is a subdirect product of prime modules. Moreover if M is a self-projective module, then M is weakly compressible if and only if it is a subdirect
product of prime modules

3. Centralizer Codes, Fateme Jafari.

    Abstract: The centralizer of an square matrix over a finite field is a linear code called centralizer code. The parity check matrix and the automorphism group of centralizer codes are studied. Specially, the structure of the centralizer code related to a cyclic matrix is discussed.

4. Quasi-cylic Codes of Index 2 and Skew Polynomial Rings, Lale Rahimi.

    Abstract: We present a study of factorization of the polynomial x^m-1 in M_2(F_2)[x] and we determine the period of any reversible polynomial of this polynomial ring by using skew polynomial rings. These results are applied to the construction of the class of quasi-cyclic codes and construction of the self-dual subclass.

5. Linear Constructions for DNA Codes, Hamide Sarmast.

    Abstract: In this thesis, we are going to translate, in terms of coding theory, the constraints that are arised in designing DNA codes for use in DNA computing or as bar-codes in chemical libraries. We will propose new constructions for DNA codes satisfying either a reverse-complement constraint, a GC-content constraint, or both, that are derived from additive and linear codes over four-letter alphabets. In particular, we focus on codes over GF(4), and we construct new DNA codes that are commonly better (sometimes far better) than previously known codes. We provide updated tables up to length 20 that include these codes as well as new codes constructed using a combination of lexicographic techniques and stochastic search

6. Quantum MDS Codes with Large Minimum Distance, Farzane Raeesi.

    Abstract: Using generalized Reed-Solomon codes and Hermitian construction, seven classes of quantum MDS codes are constructed. All of them provide large minimum distance and most of them are new in the sense that the parameters of quantum codes are different from all the previously known ones.