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Synopsis. For a linear code C, we explicitly describe a Nearest Neighbour decoder
DECODE: Fn C based on a standard array for C. For binary C sent via a binary symmetric
q
channel, we nd the probability Pundetect of an undetected
MATH32031 Coding Theory
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0. Introduction
Synopsis. This lecture offers a general introduction into the subject matter of Coding Theory, and as such, contains very little mathematics. We try to give some motivation and
historical examples. We conclude wit
MATH32031 Coding Theory
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2. Bounds
Synopsis. To respond to the Information Theory challenge, coding theorists want to design
families of codes which have high code rate and high relative distance. There is a trade-off
between these parameters, which is
MATH32031 Coding Theory
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3. Linear codes
Synopsis. We dene the most important class of codes called the linear codes. Their ability
to correct errors is no worse than that of general codes, but linear codes are easier to implement in practice and allow
MATH32031 Coding Theory
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Synopsis. We learn how to compare codes of different length using the code rate, R, and
the relative distance, . We plot the simple families of codes on the R plane, but are not
satised with the results. We compare Hammings appr
MATH32031 Coding Theory
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Example sheet week 1
Please attempt all questions. Solutions will be discussed in the examples class in week 2.
Not assessed do not hand in.
Week 01, example sheet
Question 1 (based on question A4 from the January 2013 exam). Co
MATH32031 Coding Theory
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1. Basic notions
Week 01, lecture 2
Synopsis. In this lecture, we begin to describe a mathematically rigorous setup for error-detecting an error-correcting codes. We introduce the relevant terminology and dene the
Hamming distanc
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Example sheet week 3
Week 03, ex-
Please attempt all questions. Solutions will be discussed in the examples class in week 4.
Not assessed do not hand in.
Question 5. Show: (a) a trivial code is a perfect linear code;
(b) a binar
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Examples class week 5
Synopsis. We went through solutions to most questions on the example sheet. This example
sheet is important as it demonstrates some ideas useful for the assessed homework.
1 1 1 0 0 0 0
1 0 0 1 1 0 0
7
.
Qu
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Example sheet week 2
To be discussed in Examples Class, week 3. Not for credit do not hand in.
Week 02, example sheet
Question 3. One of basic techniques for obtaining new codes from existing ones is known
as puncturing. It can