Coding Theory

Algebraic Geometry Codes

94B27, 94B40

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  7. Jennifer A. Davis, Algebraic geometric codes on anticanonical surfaces, PhD Thesis, University of Nebraska, 2007.[link]
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  9. Cunsheng Ding, Harald Niederreiter, and Chaoping Xing, Some new codes from algebraic curves, IEEE Trans. Inform. Theory 46 (2000), no. 7, 2638–2642.[MR]
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  13. Cem Güneri, Henning Stichtenoth, and Ihsan Taşkın, Further improvements on the designed minimum distance of algebraic geometry codes, J. Pure Appl. Algebra 213 (2009), no. 1, 87–97.[MR]
  14. Johan P. Hansen, Toric surfaces and codes, techniques and examples, Preprint Series No.1., University of Aarhus, Department of Mathematics, Aarhus, Denmark (2004), 12 pages.
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  18. David Joyner and Salahoddin Shokranian, Remarks on codes from modular curves: magma application, preprint (2004), 29 pages.[arXiv]
  19. Hans-Joachim Kroll and Rita Vincenti, PD-sets for binary RM-codes and the codes related to the Klein quadric and to the Schubert variety of PG(5,2), Discrete Math. 308 (2008), no. 2-3, 408–414.[MR]
  20. Thorsten Lagemann, Codes und automorphismen optimaler artin-schreier-turme, PhD Thesis, Ruprecht-Karls-Universität Heidelberg, 2006.
  21. Douglas A. Leonard, A weighted module view of integral closures of affine domains of type I, Adv. Math. Commun. 3 (2009), no. 1, 1-11.
  22. John Little and Hal Schenck, Toric surface codes and Minkowski sums, SIAM J. Discrete Math. 20 (2006), no. 4, 999–1014 (electronic).[MR]
  23. John Little and Ryan Schwarz, On m-dimensional toric codes, preprint (2005), 17 pages.[arXiv]
  24. John Little and Ryan Schwarz, On toric codes and multivariate Vandermonde matrices, Appl. Algebra Engrg. Comm. Comput. 18 (2007), no. 4, 349–367.[MR]
  25. Benjamin Lundell and Jason McCullough, A generalized floor bound for the minimum distance of geometric Goppa codes, J. Pure Appl. Algebra 207 (2006), no. 1, 155–164.[MR]
  26. Gretchen L. Matthews, Some computational tools for estimating the parameters of algebraic geometry codes, Coding Theory and Quantum Computing, Contemp. Math., vol. 381, Amer. Math. Soc., Providence, RI, 2005, pp. 19–26.[MR]
  27. Gretchen L. Matthews and Todd W. Michel, One-point codes using places of higher degree, IEEE Trans. Inform. Theory 51 (2005), no. 4, 1590–1593.[MR]
  28. Gary McGuire and José Felipe Voloch, Weights in codes and genus 2 curves, Proc. Amer. Math. Soc. 133 (2005), no. 8, 2429–2437 (electronic).[MR]
  29. Keith E. Mellinger, Classes of codes from quadratic surfaces of PG(3,q), Contrib. Discrete Math. 2 (2007), no. 1, 35–42 (electronic).[MR]
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  31. Diego Ruano, On the parameters of r-dimensional toric codes, Finite Fields Appl. 13 (2007), no. 4, 962–976.[MR]
  32. John A. Ryan and Kondwani Magamba, Equivalent irreducible Goppa codes and the precise number of quintic Goppa codes of length 32, AFRICON 2007 (2007), 1-4.[doi]
  33. Pawel Wocjan, Brill-Noether algorithm construction of geometric Goppa codes and absolute factorization of polynomials, PhD Thesis, Institut für Algorithmen und Kognitive Systeme, Universität Karlsruhe, 1999.
  34. Stephen S. -T. Yau and Huaiqing Zuo, Notes on classification of toric surface codes of dimension 5, Appl. Algebra Engrg. Comm. Comput. 20 (2009), no. 2, 175–185.[MR/doi]
  35. Marcos Zarzar, Error-correcting codes on low rank surfaces, Finite Fields Appl. 13 (2007), no. 4, 727–737.[MR]