mathematics

Rom Varshamov

Rom Varshamov is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Rom Varshamov rather than just read about it. In short: Rom Rubenovich Varshamov (Russian: Ром Рубенович Варшамов; Born April 9, 1927, in Tbilisi; Died August 24, 1999, in Moscow) was a Soviet Armenian mathematician who worked in coding theory, especially on error-correcting codes and number theory. Varshamov studied in Tbilisi with Arnold Walfisz (where he was Georgian students’ champion in the 100 metres), as well as in Tomsk.

Key takeaways

Rom Varshamov belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Rom Varshamov to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Rom Varshamov from memory before moving on to harder problems.

Reference excerpt

Rom Rubenovich Varshamov (Russian: Ром Рубенович Варшамов; Born April 9, 1927, in Tbilisi; Died August 24, 1999, in Moscow) was a Soviet Armenian mathematician who worked in coding theory, especially on error-correcting codes and number theory. Varshamov studied in Tbilisi with Arnold Walfisz (where he was Georgian students’ champion in the 100 metres), as well as in Tomsk. After that, he was a researcher in Moscow at the Steklov Institute of Mathematics with Ivan Matveyevich Vinogradov, especially on Number theory and Coding theory, and the Ministry of Radio Engineering (working in Cryptography). In 1957 he proved the Gilbert-Varshamov bound for linear codes (independently of Edgar Gilbert who proved the non-linear part). From 1968 he worked in Yerevan and was director of the Computer Centre (now Institute for Informatics and Automation Problems) of the Academy of Sciences of the Armenian SSR. He was author and co-author of more than 25 scientific articles and also a member of the Armenian National Academy of Sciences.

Selected bibliography Varshamov, R. R.: Estimate of the number of signals in error correcting codes (Russian), Dokl. Akad. Nauk SSSR 117, 739–741, 1957 (English Translation in I. F. Blake: Algebraic Coding Theory: History and Development, Dowden, Hutchinson & Ross, 1973, pp 68–71) Varshamov, R. R.: A class of codes for symmetric channels and a problem from the additive theory of numbers, IEEE Trans. Inf. Theory 19, 92–95, 1973 Varshamov, R. R.: On a method in the theory of reducibility of polynomials over a finite field, Sov. Math., Dokl. 44, No.1, 194–199, 1992; translation from Dokl. Akad. Nauk SSSR 319, No.4, 787-791, 1991

References

External links Varshamov on mathnet.ru Article in Golos Armenii, April 10, 2007, electronic version No. 142 of 26.12.09

Worked examples

Example 1 — a first encounter with Rom Varshamov

Start with the simplest possible case. Write down what Rom Varshamov claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Rom Varshamov before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Rom Varshamov ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Rom Varshamov

In research: Rom Varshamov appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Rom Varshamov in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Rom Varshamov is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1927 births, 1999 deaths, 20th-century Armenian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Rom Varshamov outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Rom Varshamov in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Rom Varshamov means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Rom Varshamov out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Rom Varshamov in simple terms?

Why does Rom Varshamov matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Rom Varshamov?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Rom Varshamov.