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Mathematics
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Codes, Designs, Cryptography and Optimization, 3rd Edition
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Codes, Designs, Cryptography and Optimization, 3rd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 31 March 2026 | Viewed by 2006

Special Issue Editor

Dr. Raúl M. Falcón

E-Mail Website
Guest Editor
Department of Applied Mathematics I, University of Seville, 41012 Sevilla, Spain
Interests: discrete mathematics; graph theory; combinatorics; computational geometry; Latin squares
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to publish original research articles covering recent advances in any of the areas included in coding theory, cryptography, combinatorial design, and combinatorial optimization, with particular emphasis on establishing new synergies among them and new applications to other fields and to the real world, including algebraic geometry, artificial intelligence, communication networks, computer science, hardware and software design, design of experiments, logistics, machine learning, and scheduling or transportation networks, among others.

Potential topics of this Special Issue include, but are not limited to, the following:

  • Algebraic coding theory;
  • Algorithm design and analysis;
  • Block design theory;
  • Computational complexity;
  • Discrete structures: enumeration and classification;
  • Error-correcting and error-detecting codes;
  • Finite geometry;
  • Graph theory;
  • Modeling combinatorial optimization problems;
  • Network design and analysis;
  • Orthogonal arrays;
  • Pseudorandom sequences;
  • Quantum cryptography;
  • Quasigroup theory;
  • Secret sharing schemes.

Dr. Raúl M. Falcón
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • association schemes
  • block design
  • cryptosystems
  • difference sets
  • Hadamard matrices
  • Latin squares
  • lattices
  • matroids
  • networks
  • orthogonal arrays

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Further information on MDPI's Special Issue policies can be found here.

Related Special Issue

Published Papers (2 papers)

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Research

12 pages, 1174 KiB  
Article
Quantum Surface Topological Code for Bell State Stabilization in Superconducting Physical Qubit Systems
by Jordi Fabián González-Contreras, Erik Zamora, Jesús Yaljá Montiel-Pérez, Juan Humberto Sossa-Azuela, Elsa Rubio-Espino and Víctor Hugo Ponce-Ponce
Mathematics 2025, 13(13), 2041; https://doi.org/10.3390/math13132041 - 20 Jun 2025
Viewed by 973
Abstract
Stabilizing quantum states in physical qubits quantum computers has been a widely explored topic in the Noisy Intermediate-Scale Quantum era. However, much of this work has focused on simulation rather than practical implementation. In this study, an experimental advancement in Bell state stabilization [...] Read more.
Stabilizing quantum states in physical qubits quantum computers has been a widely explored topic in the Noisy Intermediate-Scale Quantum era. However, much of this work has focused on simulation rather than practical implementation. In this study, an experimental advancement in Bell state stabilization is presented, which utilizes surface codes for quantum error correction across three quantum computers: ibm_fez, ibm_torino, and ibm_brisbane. Our findings indicate that error correction produces an improvement of approximately 3% in accuracy for 127-qubit systems while demonstrating a more significant enhancement of around 20% for 156-qubit systems in stabilizing the Bell state with fidelity up to 0.6 in all the experiments. This paper outlines the methodology for implementing this strategy in other applications, offering a pathway to improve results (≈20%) when experimenting with superconducting quantum computers. Full article
(This article belongs to the Special Issue Codes, Designs, Cryptography and Optimization, 3rd Edition)
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41 pages, 477 KiB  
Article
Linear-Time Polynomial Holographic Interactive Oracle Proofs with Logarithmic-Time Verification for Rank-1 Constraint System from Lookup Protocol
by Shuangjun Zhang
Mathematics 2025, 13(8), 1309; https://doi.org/10.3390/math13081309 - 16 Apr 2025
Viewed by 621
Abstract
Modern SNARKs are constructed using polynomial Interactive Oracle Proofs (IOPs) and polynomial commitments. In this work, we introduce a novel polynomial holographic IOP for the NP-Complete language Rank-1 Constraint System (R1CS), where holographic IOP means that the proof system supports preprocessing. Our [...] Read more.
Modern SNARKs are constructed using polynomial Interactive Oracle Proofs (IOPs) and polynomial commitments. In this work, we introduce a novel polynomial holographic IOP for the NP-Complete language Rank-1 Constraint System (R1CS), where holographic IOP means that the proof system supports preprocessing. Our construction achieves linear-time proving, logarithmic-time verification, and constant query complexity. For an R1CS instance with size O(N) over a sufficiently large finite field, the prover’s time is O(N), the verifier’s time is O(log N), and the query complexity is O(1). By combining our polynomial holographic IOP with the recent polynomial commitment scheme Orion, we obtain a transparent SNARK for R1CS with remarkable performance: the prover’s time is O(N), the verifier’s time is O(log2N), and the proof size is O(log2N). The core technique in our construction is the classical SumCheck protocol, which enables us to efficiently check whether an n-variate polynomial sums to a specific value on a given domain, such as {0, 1}n. Additionally, we showcase how to achieve holography from the lookup protocol, which allows us to efficiently verify that all elements in a vector are contained in another vector. We introduce a new polynomial IOP for the lookup relation with a linear-time prover. Full article
(This article belongs to the Special Issue Codes, Designs, Cryptography and Optimization, 3rd Edition)
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