Gröbner Bases, Coding, and Cryptography

1. Gröbner Bases, Coding, and Cryptography: aGuide to the State-of-Art
Massimiliano Sala

2. Gröbner Technology
Teo Mora

3. The FGLM Problem and Möller’s Algorithm onZero-dimensional Ideals
Teo Mora

4. An Introduction to Linear and Cyclic Codes
Daniel Augot, Emanuele Betti, Emmanuela Orsini

5. Decoding Cyclic Codes: the Cooper Philosophy
Teo Mora, Emmanuela Orsini

6. A Tutorial on AG Code Construction fromaGröbner Basis Perspective
Douglas A. Leonard

7. Automorphisms and Encoding of AG and Order Domain Codes
John B. Little

8. Algebraic Geometry Codes from Order Domains
Olav Geil

9. The BMS Algorithm
Shojiro Sakata

10. The BMS Algorithm and Decoding of AG Codes
Shojiro Sakata

11. A Tutorial on AG Code Decoding fromaGröbner Basis Perspective
Douglas A. Leonard

12. FGLM-Like Decoding: from Fitzpatrick’s Approach to Recent Developments
Eleonora Guerrini, Anna Rimoldi

13. An Introduction to Ring-Linear Coding Theory
Marcus Greferath

14. Gröbner Bases over Commutative Rings and Applications to Coding Theory
Eimear Byrne, Teo Mora

15. Overview of Cryptanalysis Techniques inMultivariate Public Key Cryptography
Olivier Billet, Jintai Ding

16. A Survey on Polly Cracker Systems
Françoise Levy-dit-Vehel, Maria Grazia Marinari, Ludovic Perret, Carlo Traverso

17. Block Ciphers: Algebraic Cryptanalysis andGröbner Bases
Carlos Cid, Ralf-Philipp Weinmann

18. Algebraic Attacks on Stream Ciphers withGröbner Bases
Frederik Armknecht, Gwenolé Ars

19. Canonical Representation of Quasicyclic Codes Using Gröbner Bases Theory
Kristine Lally

20. About the nth-Root Codes: a Gröbner Basis Approach to the Weight Computation
Marta Giorgetti

21. Decoding Linear Error-Correcting Codes uptoHalf the Minimum Distance with Gröbner Bases
Stanislav Bulygin, Ruud Pellikaan

22. Gröbner Bases for the Distance Distribution ofSystematic Codes
Eleonora Guerrini, Emmanuela Orsini, Ilaria Simonetti

23. A Prize Problem in Coding Theory
Jon-Lark Kim

24. An Application of Möller’s Algorithm to Coding Theory
M. Borges-Quintana, M. A. Borges-Trenard, E. Martínez-Moro

25. Mattson Solomon Transform and Algebra Codes
Edgar Martínez-Moro, Diego Ruano

26. Decoding Folded Reed–Solomon Codes Using Hensel-Lifting
Peter Beelen, Kristian Brander

27. A Note on the Generalisation oftheGuruswami–Sudan List Decoding AlgorithmtoReed–Muller Codes
Daniel Augot, Michael Stepanov

28. Viewing Multipoint Codes as Subcodes ofOne-Point Codes
Gretchen L. Matthews

29. A Short Introduction to Cyclic Convolutional Codes
Heide Gluesing-Luerssen, Barbara Langfeld, Wiland Schmale

30. On the Non-linearity of Boolean Functions
Ilaria Simonetti

31. Quasigroups as Boolean Functions, TheirEquation Systems and Gröbner Bases
D. Gligoroski, V. Dimitrova, S. Markovski

32. A New Measure to Estimate Pseudo-Randomness of Boolean Functions andRelations with Gröbner Bases
Danilo Gligoroski, Smile Markovski, Svein Johan Knapskog

33. Radical Computation for Small Characteristics
Ryutaroh Matsumoto

Keywords: Mathematics, Theory of Computation, Mathematics of Computing, Data Encryption, Combinatorics, Algebra