Беларуская: Observe the field
Беларуская: We collect decisions from spreadsheets, paper, conversations, and experienced staff. Exceptions and hidden priorities are part of the actual operation.
Беларуская: INPUT / Current workCOMPANY & ORIGIN
Беларуская: Turn mathematics into
Беларуская: software that works
Беларуская: in the field.
Беларуская: Finite Field is named after the mathematical structure known as a finite field. We organize complex conditions into consistent models and implement them as web and app systems people can use every day.
- FOUNDED
- Беларуская: January 6, 2022
- BASE
- Беларуская: Usa City, Oita Prefecture
- FOCUS
- Беларуская: From mathematical models to web and apps
INTERACTIVE / PRIME FIELDF5
2 x 3 = 6F5: 1
Legal nameFinite Field, K.K.
Business focusБеларуская: Mathematical systems development
Canonical pageБеларуская: The new company profile is handled at /about/.
Беларуская: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
WHY WE EXIST
Беларуская: Before building, make the problem solvable.
Беларуская: Operational problems do not start as formulas. We first turn human judgment, exceptions, and implicit priorities into conditions and objectives that can be compared.
Беларуская: Separate constraints and goals
Беларуская: We separate hard constraints from indicators to improve, making contradictions and missing data visible before calculation.
Беларуская: MODEL / Constraints and evaluationБеларуская: Implement a usable system
Беларуская: We do not stop at a calculation result. Input, review, correction, and sharing are implemented as web and mobile apps.
Беларуская: OUTPUT / Operating system
OUR PURPOSE
Беларуская: We use mathematics to organize ambiguous judgment into systems that can be compared, explained, and used.
THE NAME
Беларуская: Finite Field means a finite mathematical field.
Беларуская: A finite field is a mathematical structure with a finite number of elements where addition, subtraction, multiplication, and division except by zero are defined. It is important in cryptography, error-correcting codes, and computer science.
DEFINITION / PLAIN LANGUAGE
Беларуская: Limited elements. Consistent rules. Results that stay inside the set.
Беларуская: In F5, the elements are 0, 1, 2, 3, and 4. After ordinary calculation, the remainder modulo 5 is used. That is why 2 × 3 becomes 1 rather than 6.
01Беларуская: Finite elements
Беларуская: The number of elements is a prime or a power of a prime.
02Беларуская: Closed under operations
Беларуская: Results return to elements in the same field.
03Беларуская: Inverses exist
Беларуская: Every nonzero element has a multiplicative inverse.
Беларуская: Important
Беларуская: This does not mean that business operations are literally finite fields. The connection here is a company metaphor for how we work.
INTERACTIVE / PRIME FIELD
F5Беларуская: Try finite-field calculation
+
=
Беларуская: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
Беларуская: See limited resources
Беларуская: People, time, vehicles, machines, and budget. We search for plans that can actually run within real limits.
Беларуская: Make rules consistent
Беларуская: We organize business rules including exceptions so contradictions and priorities can be reviewed.
Беларуская: Make results reproducible
Беларуская: The path from inputs, constraints, and evaluation to the result should not depend only on one person’s intuition.
WHAT WE DO
Беларуская: From mathematical models to business screens.
Беларуская: We are not only a mathematical consulting team, and not only a general contract developer. We design the decision logic and the software used every day as one system.
01 / MODEL
MATHEMATICAL MODEL
01 / MODELБеларуская: What must be kept and what should improve
Беларуская: We organize constraints, objectives, priorities, exceptions, and feasibility.
02 / SOLVE
ALGORITHM
02 / SOLVEБеларуская: Search and compare candidates
Беларуская: Optimization, search, rules, and simulation are combined when appropriate.
03 / BUILD
PRODUCT ENGINEERING
03 / BUILDБеларуская: Enter, adjust, and share in the field
Беларуская: Web, iOS, Android, databases, permissions, and reports are implemented together.
INPUT
OUTPUT
OPERATING PRINCIPLES
Беларуская: Be honest before being mathematical.
Беларуская: We do not hide problems behind advanced terms or complex models. We separate what is unknown, not yet measured, and dependent on conditions.
Беларуская: Start with field language
Беларуская: We listen to actual work, decisions, and exceptions before applying terminology. A model is useful only when it explains the field.
Беларуская: Field to conditionsБеларуская: Results with reasons
Беларуская: We do not stop at “the AI decided.” We show why a plan was chosen and what could not be satisfied.
Беларуская: Result to evidenceБеларуская: Verify small before growing
Беларуская: Before production, we test the calculation on a small portion of real data. Reasons it cannot be solved are also findings.
Беларуская: Hypothesis to verificationБеларуская: Implement usability too
Беларуская: We design for input, correction, smartphone use, and multilingual operation, not only calculation speed.
Беларуская: Logic to adoptionWE SAYБеларуская: Organize conditions and create comparable plans
WE SHOWБеларуская: Inputs, constraints, evaluation, and unresolved points
WE DO NOT CLAIMБеларуская: Absolutely no bugs or always one unique optimum
COMPANY JOURNEY
Беларуская: Deepening from implementation strength into mathematics.
Беларуская: Experience building business systems, mobile apps, and multilingual services connects to planning, assignment, search, and verification.
2022.01.06FOUNDATION
FOUNDATION
Беларуская: Finite Field, K.K. established
Беларуская: Established in Usa City, Oita Prefecture, with a foundation for planning, building, and operating web, app, and business systems.
BUILDIMPLEMENTATION
NOWMATHEMATICAL SYSTEMS
MATHEMATICAL SYSTEMS
Беларуская: Toward automation of planning and assignment
Беларуская: Shift planning, visit scheduling, routing, production planning, and assignment matching are now presented as core mathematical-systems domains.
R&DVERIFY
FROM CODE TO FIELD
Беларуская: Show working assets, not only philosophy.
Беларуская: A company page alone is not enough to judge capability. Demos, business screens, case studies, and security policies are available before consultation.
01 / DEMO
Беларуская: Mathematical demos
Беларуская: Change conditions and review results and unresolved points.
Беларуская: Try 02 / CASESБеларуская: Case studies
Беларуская: Implemented functions and confirmed changes are separated.
Беларуская: Read 03 / SECURITYБеларуская: Data handling
Беларуская: Receipt, retention, external AI, deletion, and responsibility are explained.
Беларуская: Check 04 / RESEARCHMath Lab
Беларуская: Research-stage technology is separated from completed products.
Беларуская: ViewCOMPANY PROFILE
Finite Field, K.K.
Беларуская: Based in Usa City, Oita Prefecture, we design and build mathematical models, algorithms, web systems, and mobile apps.
BASE / JAPANБеларуская: Usa City, Oita Prefecture
FINITE FIELDБеларуская: Usa City, Oita Prefecture
BASE / JAPAN
Беларуская: From a regional base, we use software to address complex operational problems.
- Беларуская: Legal name
- Finite Field, K.K. / 株式会社ファイナイトフィールド
- Беларуская: Japanese name
- 株式会社ファイナイトフィールド
- Беларуская: Address
- 879-0151 Oita, Usa, Miyaguma 550, Японія
- Беларуская: Established
- Беларуская: January 6, 2022
- Беларуская: Capital
- Беларуская: JPY 3,000,000
- Беларуская: Officers
- Прадстаўнічы дырэктар Toshiya Kazuyoshi Кіраўніца Yoshie Kazuyoshi Кіраўнік Hikaru Ono
- Беларуская: Major client
- Matsuhisa Japan Co., Ltd.
- Беларуская: Business domains
- Беларуская: Mathematical systems development Web and mobile app development Business systems and R&D
INFORMATION POLICY
Беларуская: Only information aligned with official company facts is shown. Unconfirmed employee count, sales, certification status, and similar claims are not listed.
PAGE DATA REVIEWED / 2026.06FAQ
Беларуская: About the company and the name
Беларуская: A short explanation of the relationship between a mathematical term and the actual service.
01Беларуская: What is a finite field?
Беларуская: A finite field is a mathematical structure with a finite number of elements. Addition, subtraction, multiplication, and division except by zero are defined, and the result stays inside the same set. This page visualizes prime fields Fp for prime p.
02Беларуская: How does the name relate to business systems?
Беларуская: It does not mean that business operations are literally finite fields. The name reflects how we work with limited resources, consistent rules, and reproducible results.
03Беларуская: Can we start with a mathematical consultation only?
Беларуская: Yes. We can begin by checking whether operational judgments, assignments, orders, and plans can be modeled. A small calculation prototype can verify the idea first.
04Беларуская: Can you develop the actual system too?
Беларуская: Yes. We design and build mathematical models, calculation logic, databases, web admin screens, and iOS and Android apps as one delivery path.
START WITH THE PROBLEM
Беларуская: What does your team think through every time?
Беларуская: Shifts, visits, routes, production, and assignments. We start from your current spreadsheets and rules to identify what can be modeled.