@@ -13,3 +13,5 @@ *.snm
 *.vrb
 galois-theory-notes.bib
 commutative-algebra-notes.bib
+algebraic-coding-theory-notes.bib
+pinocchio-groth16.bib

@@ -1,14 +0,0 @@
-%% LaTeX2e file `algebraic-coding-theory-notes.bib'
-%% generated by the `filecontents' environment
-%% from source `algebraic-coding-theory-notes' on 2026/03/29.
-%%
-@misc{hill,
-  author = {Raymond Hill},
-  title = {{A First Course in Coding Theory}},
-  year = {1986}
-}
-@misc{lint,
-  author = {J.H. van Lint},
-  title = {{Introduction to Coding Theory}},
-  year = {1981}
-}

@@ -1,23 +0,0 @@
-%% LaTeX2e file `pinocchio-groth16.bib'
-%% generated by the `filecontents' environment
-%% from source `pinocchio-groth16' on 2026/03/31.
-%%
-@misc{cryptoeprint:2013/279,
-  author = {Bryan Parno and Craig Gentry and Jon Howell and Mariana Raykova},
-  title = {Pinocchio: Nearly Practical Verifiable Computation},
-  howpublished = {Cryptology {ePrint} Archive, Paper 2013/279},
-  year = {2013},
-  url = {https://eprint.iacr.org/2013/279}
-}
-@misc{cryptoeprint:2016/260,
-  author = {Jens Groth},
-  title = {On the Size of Pairing-based Non-interactive Arguments},
-  howpublished = {Cryptology {ePrint} Archive, Paper 2016/260},
-  year = {2016},
-  url = {https://eprint.iacr.org/2016/260}
-}
-
-@misc{pairings,
-  note = {\url{https://github.com/arnaucube/math/blob/master/weil-pairing.pdf}},
-  url = {https://github.com/arnaucube/math/blob/master/weil-pairing.pdf}
-}

@@ -167,7 +167,7 @@ \end{aligned}
 $$
 Where $5 w_3 = w_1 \cdot 2w_1$ is the constraint that we wanted to represent in the R1CS format.
 
-The nice thing from R1CS is that allows us to standarize the constraints in an equation fashion, where all the signals are involved and we 'activate' these ones that are used in each constraint.
+The nice thing from R1CS is that allows us to standaridze the constraints in an equation fashion, where all the signals are involved and we 'activate' these ones that are used in each constraint.
 Since we have now the constraints in a polynomial format, we can do work with it in the polynomial way.
 
 
@@ -337,6 +337,8 @@ $$e([a(\tau)]_1, [b(\tau)]_2) \stackrel{?}{=} e([q(\tau)]_1, [z(\tau)]_2) \cdot e([c(s)]_1, [1]_2)$$
 	which ensures that $\exists~ q(X) \in \mathbb{F}[X] ~\text{s.th.}~ a(X) b(X) - c(X) = q(X) z(X)$.
 \end{enumerate}
 
+\section{Pinocchio}
+\section{Groth16}
 
 \vspace{1cm}