Perfect Combinatorial Structures in Coding Theory and Cryptography
Abstract
This book develops algebraic and combinatorial methods for studying discrete structures. It brings together graph theory, Boolean functions, Fourier analysis on finite groups, coding theory, perfect colorings and perfect codes, association schemes, Latin squares, and related topics. A central theme is the interaction between different representations of the same object: combinatorial, algebraic, spectral, and coding-theoretic. The main mathematical object studied in this book is a perfect coloring of a graph, or, equivalently, an equitable partition of a graph. The book is intended for advanced undergraduate and graduate students in mathematics and computer science, as well as for researchers in discrete mathematics, combinatorics, coding theory, and related fields.
Related
- Fractal Hyper-Trees: Combinatorial Enumeration, Symmetry Properties, and Ultrametric Structures
- MATRIX THEORETIC AND COMBINATORIAL STRUCTURES IN ADDITION CHAINS
- Compact generation and perfect objects in homotopy categories of exact model structures
- Singular Hodge theory for combinatorial geometries
- An Algebraic Framework for Data Systems: Classification and Optimization of Algebraic Structures for Data Organization and Coding
BibTeX
@misc{potapov2026perfect,
title = {{Perfect Combinatorial Structures in Coding Theory and Cryptography}},
author = {Vladimir N. Potapov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09225},
eprint = {2609.09225},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09225},
}
RIS
TY - UNPB
TI - Perfect Combinatorial Structures in Coding Theory and Cryptography
AU - Vladimir N. Potapov
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.09225
UR - https://arxiv.org/abs/2609.09225
AB - This book develops algebraic and combinatorial methods for studying discrete structures. It brings together graph theory, Boolean functions, Fourier analysis on finite groups, coding theory, perfect colorings and perfect codes, association schemes, Latin squares, and related topics. A central theme is the interaction between different representations of the same object: combinatorial, algebraic, spectral, and coding-theoretic. The main mathematical object studied in this book is a perfect coloring of a graph, or, equivalently, an equitable partition of a graph. The book is intended for advanced undergraduate and graduate students in mathematics and computer science, as well as for researchers in discrete mathematics, combinatorics, coding theory, and related fields.
ER -