Koji Imamura

Matroid Theory / Coding Theory / Combinatorics

I study how replacing fields with finite rings reveals matroid representations and code structures that do not appear over fields. The main thread runs through representation problems over finite rings, modular independence, and q-polymatroids, with current focus on representability over finite chain rings and related critical problems.

Research overview Full publications list

Current status

Current appointment: Institute of Mathematics for Industry, Kyushu University / Research Assistant Professor

Collaboration and talks: Collaboration inquiries, invited talks, and research questions are welcome.
Student recruitment: I do not currently lead a laboratory, so I am not recruiting students.

CV: positions / grants Collaboration contact

Latest preprint

On Representing Matroids via Modular Independence (arXiv / 2026)

A representative entry point to the current main direction, tying finite-ring representability to code correspondences.

Publication entry PDF arXiv

Research Overview

A three-point overview of the question, the approach, and why this work matters.

Question
When the base algebra is changed from a field to a finite ring, one encounters matroids that are not representable over fields, together with independence notions arising from local rings. I ask how these finite-ring phenomena appear in matroid representations.
Approach
I study representation problems over finite rings together with q-polymatroids, finite geometry, and code correspondences, in order to compare representations, study extensions, and isolate structures related to optimal codes.
Why it matters
This viewpoint helps explain discrete structures that are harder to see over fields, and provides combinatorial language for understanding known optimal codes and organising candidates for new constructions.

See the full research overview Current Directions

Representative Papers

On the home page, the same three papers are ordered so the research thesis can be grasped quickly: current direction first, then the q-polymatroid side, then the coding-theory side.

What These Papers Show

Together, the three papers give a compact view of the current thesis: finite-ring representability, the q-polymatroid formulation, and the coding-theoretic quantitative side.

Closest to the Current Direction
arXiv preprint arXiv:2603.08016, 2026
On Representing Matroids via Modular Independence
Koji Imamura, Keisuke Shiromoto
Plain-language summary
Some matroids become representable once fields are replaced by finite chain rings. This paper explains how to recognise that situation and how it connects to codes.
Technical summary
Using modular independence over local commutative rings, it gives criteria for representability over finite chain rings and describes the correspondence with codes.
Why start here
It is the clearest current entry point to the finite-ring representability side of the project and its links with codes.
What it asks
It asks which matroids are representable over finite chain rings through modular independence arising from local commutative rings.
What it shows
It gives criteria for representability over finite chain rings together with a correspondence to codes.
Why it matters
It matters because it presents finite-ring representability and code correspondences together as a central current direction.
Collaboration fit
A useful starting point for collaborations connecting representability over finite rings with coding-theoretic questions.
Read next
Then see the coding-theory side
PDF(opens in a new tab)arXiv(opens in a new tab)
Go to the full publication entry
Entry Point to q-polymatroids
Discrete Math., 347(5), Paper No. 113924, 13, 2024
Critical problem for a q-analogue of polymatroids
Koji Imamura, Keisuke Shiromoto
Plain-language summary
This paper identifies the critical problem to ask for q-polymatroids and supplies basic examples that make the framework usable.
Technical summary
It formulates the critical problem for q-polymatroids and introduces q-analogues of minimal blocks together with explicit examples.
Why start here
It provides the basic vocabulary and a concrete starting point for the q-polymatroid side of the work.
What it asks
It asks how to formulate a q-polymatroid analogue of the classical critical problem.
What it shows
It formulates the critical problem and gives q-analogues of minimal blocks together with concrete examples.
Why it matters
It matters because it supplies the basic vocabulary and a starting point for entering the q-polymatroid side.
Collaboration fit
A useful collaboration entry point around q-polymatroids, finite geometry, and the critical problem.
Read next
Then see q-matroid extendability
DOI(opens in a new tab)MathSciNet(opens in a new tab)
Go to the full publication entry
Coding-Theory Side
Finite Fields Appl., 76, Paper No. 101900, 14, 2021
Critical Problem for codes over finite chain rings
Koji Imamura, Keisuke Shiromoto
Plain-language summary
This paper gives upper bounds on how large the critical exponent of a code over a finite chain ring can be.
Technical summary
It studies the critical problem for codes over finite chain rings and proves upper bounds for the critical exponent.
Why start here
On the coding-theory side, it most clearly shows how the project leads to concrete quantitative results.
What it asks
It asks what quantitative constraints the critical problem imposes for codes over finite chain rings.
What it shows
It establishes upper bounds for the critical exponent of codes over finite chain rings.
Why it matters
It matters because it most clearly shows the coding-theory side leading to a concrete quantitative result.
Collaboration fit
A useful entry point for collaborations on finite-chain-ring codes and their quantitative problems.
Read next
Then see the current finite-ring direction
DOI(opens in a new tab)MathSciNet(opens in a new tab)
Go to the full publication entry

Publications: full list

Research at a Glance

A compact view of the current direction, where to begin reading, and the research support behind the work.

Current Directions
Current work centres on representation problems over finite rings and follows how they connect to q-polymatroids and structures related to optimal codes.
Research: current directions
Start with These Two Papers
If you want the quickest entry to the current main themes, start with the two suggested papers and the reading order they provide.
Research: start with two papers
Research Support
Current grant
Construction of Optimal Codes Based on Matroid Theory and Finite GeometryJapan Society for the Promotion of Science / Project number: 25K17298
Earlier research support
JSPS Research Fellow (DC1) / Grant-in-Aid for JSPS Fellows (22KJ2512)
CV: positions / grants Grant project page Official IMI profile

Start Here by Purpose

Choose the clearest first click for collaboration, evaluation, or a first reading.

For Potential Collaborators

Use the current directions and representative papers to see the questions that are most likely to connect now, then move on to contact details.

Research: current directions Collaboration contact

For Hiring Committees

Go straight to the CV for position and support details, and to the full publications list for the research record.

CV: positions / grants Publications: full list

For First-Time Readers & Non-specialists

Start with the research overview for the question and method, then use the two suggested papers as the clearest reading order.

Research overview Start Here: Two Papers

Recent Updates

Recent papers, talks, and research-related updates.

April 2026
Presented “On matroid representations via modular independence” at Arrangement Workshop in Sapporo 2026(opens in a new tab).
March 2026
Released preprint: “On Representing Matroids via Modular Independence(opens in a new tab)”.
January 2026
Released preprint: “Periodicity of weight enumerators for codes generated by an integral matrix(opens in a new tab)”.
January 2026
Presented “On matroid representation problems via modular independence over local rings” at IMI Cryptography Seminar(opens in a new tab).
December 2025
Presented “On matroid representations via modular independence” at Designs, Codes, and Related Combinatorial Structures 2025(opens in a new tab).

Contact

For collaboration, invited talks, and research questions, use the contact Gmail; for publications and public records, use the research profiles below. Affiliation-related contact details are on the full contact page.

MathSciNet reports an Erdős number of 4(opens in a new tab).

Koji Imamura

Current status

Research Overview

Question

Approach

Why it matters

Representative Papers

On Representing Matroids via Modular Independence

Critical problem for a q-analogue of polymatroids

Critical Problem for codes over finite chain rings

Research at a Glance

Current Directions

Start with These Two Papers

Research Support

Start Here by Purpose

Recent Updates

Contact