M README.md → README.md

@@ -8,6 +8,7 @@ - [Notes on "Abstract Algebra" book, by Charles C. Pinter](abstract-algebra-charles-pinter-notes.pdf)
 - [Notes on Weil pairing](weil-pairing.pdf)
 - [Notes on Galois Theory](galois-theory-notes.pdf)
 - [Notes on Commutative Algebra](commutative-algebra-notes.pdf)
+- [Notes on Algebraic Coding Theory](algebraic-coding-theory.pdf)
 
 
 In-between math & crypto:

M algebraic-coding-theory-notes.pdf → algebraic-coding-theory-notes.pdf

M algebraic-coding-theory-notes.tex → algebraic-coding-theory-notes.tex

@@ -198,7 +198,7 @@ where $I_k$ is the $k \times k$ identity matrix, and $A$ is a $k \times (n-k)$ matrix.
 \end{thm}
 
 \subsection{Encoding with a linear code}
-Let $C$ a $[n,k]$-code over $GF(q)$ with GM $G$. $C$ contains $q^k$ codewords $\Longrightarrow$ can be used to comunicate any one of $q^k$ distinct messages.
+Let $C$ a $[n,k]$-code over $GF(q)$ with GM $G$. $C$ contains $q^k$ codewords $\Longrightarrow$ can be used to communicate any one of $q^k$ distinct messages.
 
 Iddentify these messages with the $q^k$ tuples of $V(k,q)$.
 
@@ -345,7 +345,7 @@ \end{defn}
 
 
 \begin{thm}{6.12}[Shanon's theorem]
-  channel binary symmetric with symbol error probabiliy $p$.
+  channel binary symmetric with symbol error probability $p$.
 
   Let $R < \mathscr{C}(p)$.
 
@@ -365,7 +365,7 @@ \end{thm}
 
 \begin{eg}{6.15}
   for the code of \ref{h.6.5},
-  $$P_{undetec}(C) = \underbrace{1}_{0101} \cdot p^2 (1-p)^2 + \underbrace{2}_{1011, 1110} \cdot p^3(1-p)^{4-3=1}= p^2 -p^4$$
+  $$P_{undetec}(C) = \underbrace{1 \cdot p^2 (1-p)^2}_{0101} + \underbrace{2 \cdot p^3(1-p)^{4-3=1} }_{1011,~1110}= p^2 -p^4$$
 \end{eg}
 
 \bibliographystyle{unsrt}