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Iliya Bouyukliev

Publications and source records attributed to Iliya Bouyukliev.

11 recordsLinked to original sources
arXiv2026

Enumeration and Monotonicity of Linear Codes with Prescribed Hull Dimensions

The hull of a linear code is the intersection of the code with its dual and depends on the choice of inner product. We study how the numbers of linear codes with prescribed Euclidean, Hermitian, and symplectic hull dimensions vary with the hull dimension. Building on closed enumeration formulae, we derive exact ratio decompositions for the Hermitian and symplectic cases, determine the parameter ranges in which monotonicity holds, and identify the exceptional families. We also compare the three inner products and complement the theoretical analysis with computational classification results for quaternary codes.

math.CO↗
arXiv2025

Sequence of Numbers of Linear Codes with Increasing Hull Dimensions

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 $n\ge 2k$ 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 $k$.

cs.IT↗
arXiv2022

An Algorithm for Computing the Covering Radius of a Linear Code Based on Vilenkin-Chrestenson Transform

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.

cs.IT↗
arXiv2022

About Code Equivalence -- a Geometric Approach

The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for equivalence of linear codes, based on their relation to multisets of points in a projective geometry.

cs.DM↗
arXiv2020

Computer classification of linear codes

We present algorithms for classification of linear codes over finite fields, based on canonical augmentation and on lattice point enumeration. We apply these algorithms to obtain classification results over fields with 2, 3 and 4 elements. We validate a correct implementation of the algorithms with known classification results from the literature, which we partially extend to larger ranges of parameters.

cs.IT↗
arXiv2019

Characteristic vector and weight distribution of a linear code

We develop an algorithm for computing the weight distribution of a linear $[n,k]$ code over a finite field $\mathbb{F}_q$. We represent the codes by their characteristic vector with respect to a given generator matrix and a special type of a generator matrix of the k-dimensional simplex code. This characteristic vector is the input data of our algorithms. The complexity of the presented algorithms is O(kq^k).

cs.DM↗
arXiv2012

Some Extremal Self-Dual Codes and Unimodular Lattices in Dimension 40

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.

math.CO↗
arXiv2010

Results on Binary Linear Codes With Minimum Distance 8 and 10

All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact bounds for binary linear codes. Primarily two algorithms considering the dual codes are used, namely extension of dual codes with a proper coordinate, and a fast algorithm for finding a maximum clique in a graph, which is modified to find a maximum set of vectors with the right dependency structure.

cs.IT↗
arXiv2008

Binary and Ternary Quasi-perfect Codes with Small Dimensions

The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of infinite families of QP codes which includes all binary, ternary and quaternary codes known to is. We continue further with a list of sporadic examples of binary and ternary QP codes. Later we present the results of our investigation where binary QP codes of dimensions up to 14 and ternary QP codes of dimensions up to 13 are classified.

math.CO↗