Papers by Stefka Bouyuklieva
arXiv (Cornell University), Feb 2, 2024
The hull of a linear code C is the intersection of C with its dual code. We present and analyze t... more The hull of a linear code C is the intersection of C with its dual code. We present and analyze the number of linear q-ary codes of the same length and dimension but with different dimensions for their hulls. We prove that for given dimension k and length n ≥ 2k the number of all [n, k] q linear codes with hull dimension l decreases as l increases. We also present classification results for binary and ternary linear codes with trivial hulls (LCD and self-orthogonal) for some values of the length n and dimension k, comparing the obtained numbers with the number of all linear codes for the given n and k.
Mathematics, Feb 26, 2022
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
arXiv (Cornell University), Feb 24, 2022
We present a generalization of Walsh-Hadamard transform that is suitable for applications in Codi... more We present a generalization of Walsh-Hadamard transform that is suitable for applications in Coding Theory, especially for computation of the weight distribution and the covering radius of a linear code over a finite field. The transform used in our research, is a modification of Vilenkin-Chrestenson transform. Instead of using all the vectors in the considered space, we take a maximal set of nonproportional vectors, which reduces the computational complexity.
Serdica Journal of Computing, Nov 3, 2017
Mathematics, Dec 3, 2022
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Serdica Journal of Computing, Nov 3, 2017
In this article, we study two representations of a Boolean function which are very important in t... more In this article, we study two representations of a Boolean function which are very important in the context of cryptography. We describe Möbius and Walsh Transforms for Boolean functions in details and present effective algorithms for their implementation. We combine these algorithms with the Gray code to compute the linearity, nonlinearity and algebraic degree of a vectorial Boolean function. Such a detailed consideration will be very helpful for students studying the design of block ciphers, including PhD students in the beginning of their research.
Mathematics, Sep 22, 2021
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
arXiv (Cornell University), Jul 24, 2019
We propose an algorithm for classification of linear codes over different finite fields based on ... more We propose an algorithm for classification of linear codes over different finite fields based on canonical augmentation. We apply this algorithm to obtain classification results over fields with 2, 3 and 4 elements.
arXiv (Cornell University), Nov 10, 2011
In this paper, binary extremal singly even self-dual codes of length 40 and extremal odd unimodul... more In this paper, binary extremal singly even self-dual codes of length 40 and extremal odd unimodular lattices in dimension 40 are studied. We give a classification of extremal singly even self-dual codes of length 40. We also give a classification of extremal odd unimodular lattices in dimension 40 with shadows having 80 vectors of norm 2 through their relationships with extremal doubly even self-dual codes of length 40.
arXiv (Cornell University), Aug 3, 2021
The aim of this work is to study the structure and properties of the binary LCD codes having an a... more The aim of this work is to study the structure and properties of the binary LCD codes having an automorphisms of odd prime order and to present a method for their construction.
IEEE Transactions on Information Theory, Oct 1, 2022
The aim of this work is to study the structure and properties of the binary LCD codes having an a... more The aim of this work is to study the structure and properties of the binary LCD codes having an automorphisms of odd prime order and to present a method for their construction.
Dual transform and projective self-dual codes
Advances in Mathematics of Communications
Finite Fields and Their Applications, Jul 1, 2007
All optimal binary self-dual codes of length 42 which have an automorphism of order 3 are constru... more All optimal binary self-dual codes of length 42 which have an automorphism of order 3 are constructed. In this way we complete the classification of [42, 21, 8] SD codes having an automorphism of odd prime order.
The aim of this work is to study the structure and properties of the binary LCD codes having an a... more The aim of this work is to study the structure and properties of the binary LCD codes having an automorphisms of odd prime order and to present a method for their construction.
arXiv (Cornell University), Jan 20, 2012
The purpose of this paper is to complete the classification of binary self-dual [48, 24, 10] code... more The purpose of this paper is to complete the classification of binary self-dual [48, 24, 10] codes with an automorphism of odd prime order. We prove that if there is a self-dual [48, 24, 10] code with an automorphism of type p-(c, f) with p being an odd prime, then p = 3, c = 16, f = 0. By considering only an automorphism of type 3-(16, 0), we prove that there are exactly 264 inequivalent self-dual [48, 24, 10] codes with an automorphism of odd prime order, equivalently, there are exactly 264 inequivalent cubic self-dual [48, 24, 10] codes.
Годишник на Шуменския университет Епископ Константин Преславски, 2022
In this work we apply the method for constructing binary LCD codes via an automorphism of prime o... more In this work we apply the method for constructing binary LCD codes via an automorphism of prime order described in [3] and [4]. Thus we obtain all optimal LCD codes of lengths 26, 27 and 28 possessing an automorphism of order 13 with two cycles.
Mathematical Software – ICMS 2020, 2020
An approach for classification of linear codes with given parameters starting from their proper r... more An approach for classification of linear codes with given parameters starting from their proper residual codes or subcodes is presented. The base of the algorithm is the concept of canonical augmentation which is important for parallel implementations. The algorithms are implemented in the programs LengthExtension and DimExtension of the package QextNewEdition. As an application, the nonexistence of binary [41, 14, 14] codes is proved.
An Algorithm for Computing the Weight Distribution of a Linear Code Over a Composite Finite Field with Characteristic 2
Recent Topics in Differential Geometry and its Related Fields, 2019
Serdica Journal of Computing, 2016
This paper presents developed software in the area of Coding Theory. Using it, all binary self-du... more This paper presents developed software in the area of Coding Theory. Using it, all binary self-dual codes with given properties can be classified. The programs have consequent and parallel implementations. ACM Computing Classification System (1998): G.4, E.4.
On the Automorphism Group of a Doubly-Even Code
Uploads
Papers by Stefka Bouyuklieva