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\begin{document}
	\title{E2 205 Error-Control Coding \\ Lecture 0}
	\author{Vinayak Ramkumar}
	\date{ August 7, 2019}
	\maketitle
	
\section{Basics of Linear Block Codes}

\bdefn
An $(n,k)_q$ linear block code is a $k$ dimensional subspace of $\mathbb{F}_q^n$.
\edefn 

\subsection{Minimum Distance of a Code}
 
\beq
W_{min} = d_{min} 
\eeq

\section{Bounds on code size}

\bit
\item Hamming bound
\beqn
q^k \le \frac{q^n}{\sum_{i=0}^{t}{n \choose i}(q-1)^i} \ ,
\eeqn
where $t=\lfloor\frac{d-1}{2} \rfloor$.
\item GV bound

\item Elias bound
\eit 

\section{Single-Parity-Check  Code}
\bean
G=
\begin{bmatrix}
	1 & 0 & 1 \\
	0 & 1 & 1  
\end{bmatrix}.
\eean 

\ \\ 
If you have any queries, please drop me (vinayak@iisc.ac.in) an email.
\end{document}
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