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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
ch
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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 s
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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. T
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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 line
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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
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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
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 introduc
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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: (
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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 th
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Example sheet week 4
Week 04, ex-
1
1
Question 10. Let C F7 be the linear code with generator matrix
2
1
0
(a) Find a generator matrix for C in standard form.
1 1 0 0 0 0
0
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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 c