[[1] N. Alon, Combinatorial Nullstellensatz, Recent trends in combinatorics (Mátraháza, 1995), Combin. Probab. Comput.8 (1999), no. 1-2, 7–29.10.1017/S0963548398003411]Search in Google Scholar
[[2] W. W. Adams and P. Loustaunau, An Introduction to Gröbner Bases, GSM 3, American Mathematical Society, 1994.10.1090/gsm/003]Search in Google Scholar
[[3] D. Cox, J. Little and D. O’Shea, Ideals, Varieties, and Algorithms, Springer-Verlag, 1992.10.1007/978-1-4757-2181-2]Search in Google Scholar
[[4] P. Delsarte, J. M. Goethals and F. J. MacWilliams, On generalized Reed-Muller codes and their relatives, Information and Control16 (1970), 403–442.10.1016/S0019-9958(70)90214-7]Search in Google Scholar
[[5] I. M. Duursma, C. Rentería and H. Tapia-Recillas, Reed-Muller codes on complete intersections, Appl. Algebra Engrg. Comm. Comput.11 (2001), no. 6, 455–462.10.1007/s002000000047]Search in Google Scholar
[[6] D. Eisenbud, The geometry of syzygies: A second course in commutative algebra and algebraic geometry, Graduate texts in Mathematics 229, Springer-Verlag, New York, 2005.10.1017/CBO9780511756382.005]Search in Google Scholar
[[7] D. Eisenbud and B. Sturmfels, Binomial ideals, Duke Math. J.84 (1996), 1–45.10.1215/S0012-7094-96-08401-X]Search in Google Scholar
[[8] A. V. Geramita, M. Kreuzer and L. Robbiano, Cayley-Bacharach scheme-sand their canonical modules, Trans. Amer. Math. Soc.339 (1993), no. 1, 163-189.10.1090/S0002-9947-1993-1102886-5]Search in Google Scholar
[[9] L. Gold, J. Little and H. Schenck, Cayley-Bacharach and evaluation codes on complete intersections, J. Pure Appl. Algebra196 (2005), no. 1, 91–99.10.1016/j.jpaa.2004.08.015]Search in Google Scholar
[[10] M. González-Sarabia, C. Rentería and H. Tapia-Recillas, Reed-Muller-type codes over the Segre variety, Finite Fields Appl.8 (2002), no. 4, 511–518.10.1006/ffta.2002.0360]Search in Google Scholar
[[11] M. González-Sarabia and C. Rentería, Evaluation codes associated to complete bipartite graphs, Int. J. Algebra2 (2008), no. 1-4, 163–170.]Search in Google Scholar
[[12] M. González-Sarabia, J. Nava, C. Rentería and E. Sarmiento, Parameterized codes over cycles, An. St. Univ. Ovidius Constanta21 (2013), no. 3, 241–255.10.2478/auom-2013-0056]Search in Google Scholar
[[13] J. Harris, Algebraic Geometry. A first course, Graduate Texts in Mathematics 133, Springer-Verlag, New York, 1992.10.1007/978-1-4757-2189-8_11]Search in Google Scholar
[[14] H. H. López, C. Rentería and R. H. Villarreal, Affine cartesian codes, Des. Codes Cryptography. 71 (2014), no. 1, 5–19.10.1007/s10623-012-9714-2]Search in Google Scholar
[[15] H. H. López, E. Sarmiento, M. Vaz Pinto and R. H. Villarreal, Parameterized a ne codes, Studia Sci. Math. Hungar.49 (2012), no. 3, 406–418.10.1556/sscmath.49.2012.3.1216]Search in Google Scholar
[[16] J. Neves, M. Vaz Pinto and R. H. Villarreal, Vanishing ideals over graphs and even cycles, Comm. Algebra43 (2015), no. 3, 1050–1075.10.1080/00927872.2012.714025]Search in Google Scholar
[[17] C. Rentería, A. Simis and R. H. Villarreal, Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields, Finite Fields Appl.17 (2011), no. 1, 81–104.10.1016/j.ffa.2010.09.007]Search in Google Scholar
[[18] A. Sørensen, Projective Reed-Muller codes, IEEE Trans. Inform. Theory37 (1991), no. 6, 1567–1576.10.1109/18.104317]Search in Google Scholar
[[19] R. Stanley, Hilbert functions of graded algebras, Adv. Math.28 (1978), 57–83.10.1016/0001-8708(78)90045-2]Search in Google Scholar
[[20] H. Stichtenoth, Algebraic function fields and codes. Universitext, Springer-Verlag, Berlin, 1993.]Search in Google Scholar
[[21] M. Tsfasman, S. Vladut and D. Nogin, Algebraic geometric codes: basic notions, Mathematical Surveys and Monographs 139, American Mathematical Society, Providence, RI, 2007.10.1090/surv/139]Search in Google Scholar
[[22] R. H. Villarreal, Monomial Algebras, Monographs and Textbooks in Pure and Applied Mathematics 238, Marcel Dekker, New York, 2001.10.1201/9780824746193]Search in Google Scholar