Parameterized Codes over Cycles

[1] W. W. Adams and P. Loustaunau, An Introduction to Grobner Bases (GSM 3, American Mathematical Society, 1994).10.1090/gsm/003Search in Google Scholar

[2] P. Delsarte, J. M. Goethals and F. J. MacWilliams, On generalized Reed- Muller codes and their relatives, Information and Control 16 (1970) 403­442.Search in Google Scholar

[3] I. M. Duursma, C. Renteria and H. Tapia-Recillas, Reed-Muller codes on complete intersections, Appl. Algebra Engrg. Comm. Comput. 11 (6) (2001) 455-462.10.1007/s002000000047Search in Google Scholar

[4] L. Gold, J. Little and H. Schenck, Cayley-Bacharach and evaluation codes on complete intersections, J. Pure Appl. Algebra 196 (1) (2005) 91-99.10.1016/j.jpaa.2004.08.015Search in Google Scholar

[5] M. Gonzalez-Sarabia and C. Renteria, Evaluation codes associated to complete bipartite graphs, Int. J. Algebra 2 (2008) 163-170.Search in Google Scholar

[6] M. Gonzalez-Sarabia, C. Renteria and M. Hernandez de la Torre, Mini­mum distance and second generalized Hamming weight of two particular linear codes, Congr. Numer. 161 (2003) 105-116.Search in Google Scholar

[7] M. Gonzalez-Sarabia, C. Renteria and H. Tapia-Recillas, Reed-Muller- type codes over the Segre variety, Finite Fields Appl. 8 (4) (2002) 511­518.10.1006/ffta.2002.0360Search in Google Scholar

[8] D. Grayson and M. Stillman, Macaulay2 (Available via anonymous ftp from math.uiuc.edu, 1996).Search in Google Scholar

[9] J. Harris, Algebraic Geometry. A first course (Graduate Texts in Mathe­matics 133, Springer-Verlag, New York, 1992).10.1007/978-1-4757-2189-8_11Search in Google Scholar

[10] F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-correcting Codes (North-Holland, 1977).Search in Google Scholar

[11] C. Renteria, A. Simis and R. H. Villarreal, Algebraic methods for param­eterized codes and invariants of vanishing ideals over finite fields, Finite Fields Appl. 17 (2011) 81-104.10.1016/j.ffa.2010.09.007Search in Google Scholar

[12] E. Reyes, R. H. Villarreal and L. Zárate, A note on affine toric varieties, Linear Algebra Appl. 318 (2000) 173-179.10.1016/S0024-3795(00)00166-XSearch in Google Scholar

[13] E. Sarmiento, M. Vaz Pinto and R. H. Villarreal, The minimum distance of parameterized codes on projective tori, Appl. Algebra Engrg. Comm. Comput. 22 (4) (2011) 249-264.10.1007/s00200-011-0148-2Search in Google Scholar

[14] C.E. Shannon, The mathematical theory of communication, Bell system technical journal 27 (1948) 379-423, 623-656.10.1002/j.1538-7305.1948.tb01338.xSearch in Google Scholar

[15] A. S0rensen, Projective Reed-Muller codes, IEEE Trans. Inform. Theory 37 (6) (1991) 1567-1576.10.1109/18.104317Search in Google Scholar

[16] R. Stanley, Hilbert functions of graded algebras, Adv. Math. 28 (1978) 57-83.10.1016/0001-8708(78)90045-2Search in Google Scholar

[17] H. Stichtenoth, Algebraic function fields and codes (Universitext, Sprin- ger-Verlag, Berlin, 1993).Search in Google Scholar

[18] 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/139Search in Google Scholar

[19] R. H. Villarreal, Monomial Algebras (Monographs and Textbooks in Pure and Applied Mathematics 238, Marcel Dekker, New York, 2001). 10.1201/9780824746193Search in Google Scholar