references.bib

% CompPoly bibliography.
%
% Every citation key used in a Lean docstring must have an entry here; see the
% "Citation Standards" section of CONTRIBUTING.md. Keys are cited from Lean as
% `[Author, *Title*][Key]` inside a `## References` block.
%
% To find keys that are cited but missing from this file:
%
%   grep -rho '\]\[[A-Za-z][A-Za-z0-9+]*\]' --include='*.lean' CompPoly/ \
%     | sort -u
%
% (That grep also matches `[...][Y]` and `[...][x]` from ordinary Lean indexing
% notation; ignore those two.)

% ---------------------------------------------------------------------------
% Coding theory: Reed-Solomon encoding and decoding
% ---------------------------------------------------------------------------

@article{GS99,
  author  = {Guruswami, Venkatesan and Sudan, Madhu},
  title   = {Improved decoding of {Reed--Solomon} and algebraic-geometry codes},
  journal = {IEEE Transactions on Information Theory},
  volume  = {45},
  number  = {6},
  pages   = {1757--1767},
  year    = {1999},
  doi     = {10.1109/18.782097}
}

@incollection{Gao02,
  author    = {Gao, Shuhong},
  title     = {A new algorithm for decoding {Reed--Solomon} codes},
  booktitle = {Communications, Information and Network Security},
  editor    = {Bhargava, Vijay K. and Poor, H. Vincent and Tarokh, Vahid and
               Yoon, Seokho},
  series    = {The Springer International Series in Engineering and Computer
               Science},
  volume    = {712},
  pages     = {55--68},
  publisher = {Springer},
  year      = {2003},
  doi       = {10.1007/978-1-4757-3789-9_5},
  note      = {Manuscript circulated from 2002; cited as \texttt{Gao02}}
}

@article{RR00,
  author  = {Roth, Ron M. and Ruckenstein, Gitit},
  title   = {Efficient decoding of {Reed--Solomon} codes beyond half the minimum
             distance},
  journal = {IEEE Transactions on Information Theory},
  volume  = {46},
  number  = {1},
  pages   = {246--257},
  year    = {2000},
  doi     = {10.1109/18.817522}
}

@article{Ale05,
  author  = {Alekhnovich, Michael},
  title   = {Linear {Diophantine} equations over polynomials and soft decoding of
             {Reed--Solomon} codes},
  journal = {IEEE Transactions on Information Theory},
  volume  = {51},
  number  = {7},
  pages   = {2257--2265},
  year    = {2005},
  doi     = {10.1109/TIT.2005.850102}
}

@article{LOS06,
  author  = {Lee, Kwankyu and O'Sullivan, Michael E.},
  title   = {List decoding of {Reed--Solomon} codes from a {Gr\"obner} basis
             perspective},
  journal = {Journal of Symbolic Computation},
  volume  = {43},
  number  = {9},
  pages   = {645--658},
  year    = {2008},
  doi     = {10.1016/j.jsc.2008.01.002},
  note    = {Preprint \texttt{arXiv:math/0601022} (2006); cited as \texttt{LOS06}}
}

@inproceedings{LCH14,
  author    = {Lin, Sian-Jheng and Chung, Wei-Ho and Han, Yunghsiang S.},
  title     = {Novel polynomial basis and its application to {Reed--Solomon}
               erasure codes},
  booktitle = {55th Annual IEEE Symposium on Foundations of Computer Science
               (FOCS)},
  pages     = {316--325},
  year      = {2014},
  doi       = {10.1109/FOCS.2014.41}
}

% ---------------------------------------------------------------------------
% Root finding, polynomial arithmetic, and linear algebra
% ---------------------------------------------------------------------------

@article{MOV92,
  author  = {Menezes, Alfred J. and van Oorschot, Paul C. and
             Vanstone, Scott A.},
  title   = {Subgroup refinement algorithms for root finding in {$GF(q)$}},
  journal = {SIAM Journal on Computing},
  volume  = {21},
  number  = {2},
  pages   = {228--239},
  year    = {1992},
  doi     = {10.1137/0221017}
}

@article{MS03,
  author  = {Mulders, Thom and Storjohann, Arne},
  title   = {On lattice reduction for polynomial matrices},
  journal = {Journal of Symbolic Computation},
  volume  = {35},
  number  = {4},
  pages   = {377--401},
  year    = {2003},
  doi     = {10.1016/S0747-7171(02)00139-6}
}

@inproceedings{GGJ96,
  author    = {von zur Gathen, Joachim and Gerhard, J\"urgen},
  title     = {Arithmetic and factorization of polynomials over {$\mathbb{F}_2$}
               (extended abstract)},
  booktitle = {Proceedings of the 1996 International Symposium on Symbolic and
               Algebraic Computation (ISSAC '96)},
  pages     = {1--9},
  publisher = {ACM},
  year      = {1996},
  doi       = {10.1145/236869.236882},
  note      = {Cited in the Lean sources as \texttt{GGJ96}}
}

@book{Lan02,
  author    = {Lang, Serge},
  title     = {Algebra},
  edition   = {3},
  series    = {Graduate Texts in Mathematics},
  volume    = {211},
  publisher = {Springer},
  year      = {2002},
  doi       = {10.1007/978-1-4613-0041-0}
}

% ---------------------------------------------------------------------------
% Binary towers
% ---------------------------------------------------------------------------

@misc{DP23,
  author       = {Diamond, Benjamin E. and Posen, Jim},
  title        = {Succinct arguments over towers of binary fields},
  howpublished = {Cryptology ePrint Archive, Paper 2023/1784},
  year         = {2023},
  url          = {https://eprint.iacr.org/2023/1784}
}

@misc{DP24,
  author       = {Diamond, Benjamin E. and Posen, Jim},
  title        = {Polylogarithmic proofs for multilinears over binary towers},
  howpublished = {Cryptology ePrint Archive, Paper 2024/504},
  year         = {2024},
  url          = {https://eprint.iacr.org/2024/504}
}

% ---------------------------------------------------------------------------
% Cited from docs/wiki/field-extensions.md rather than a Lean docstring.
% TODO: fill in author and title from the ePrint before relying on this entry.
% ---------------------------------------------------------------------------

@misc{ABF26,
  title        = {Cryptology ePrint Archive, Paper 2026/680},
  howpublished = {Cryptology ePrint Archive, Paper 2026/680},
  year         = {2026},
  url          = {https://eprint.iacr.org/2026/680},
  note         = {Parameter point behind ArkLib's \texttt{KoalaSextic};
                  author list and title not yet transcribed}
}