Ghorpade, Sudhir R.; Ludhani, Rati On the purity of resolutions of Stanley-Reisner rings associated to Reed-Muller codes. (English) Zbl 1523.13035 Ashraf, Mohammad (ed.) et al., Algebra and related topics with applications, ICARTA-2019, Aligarh, India, December 17–19, 2019. Singapore: Springer. Springer Proc. Math. Stat. 392, 325-335 (2022). MSC: 13F55 94B15 PDFBibTeX XMLCite \textit{S. R. Ghorpade} and \textit{R. Ludhani}, Springer Proc. Math. Stat. 392, 325--335 (2022; Zbl 1523.13035) Full Text: DOI arXiv
Hodges, Timothy J.; Iyer, Hari R. Semi-regularity of pairs of Boolean polynomials. (English) Zbl 1492.13002 Finite Fields Appl. 79, Article ID 101992, 37 p. (2022). Reviewer: Manjit Singh (Murthal) MSC: 13A02 11T55 12E05 12E20 13M10 94A60 PDFBibTeX XMLCite \textit{T. J. Hodges} and \textit{H. R. Iyer}, Finite Fields Appl. 79, Article ID 101992, 37 p. (2022; Zbl 1492.13002) Full Text: DOI
Hegedüs, Gábor; Rónyai, Lajos An upper bound for the size of \(s\)-distance sets in real algebraic sets. (English) Zbl 1467.05267 Electron. J. Comb. 28, No. 3, Research Paper P3.27, 11 p. (2021). MSC: 05D40 05B30 05E30 14P05 05B20 05B25 05D05 13P10 PDFBibTeX XMLCite \textit{G. Hegedüs} and \textit{L. Rónyai}, Electron. J. Comb. 28, No. 3, Research Paper P3.27, 11 p. (2021; Zbl 1467.05267) Full Text: DOI arXiv
López, Hiram H.; Soprunov, Ivan; Villarreal, Rafael H. The dual of an evaluation code. (English) Zbl 1469.13057 Des. Codes Cryptography 89, No. 7, 1367-1403 (2021). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 13P25 14G50 94B27 11T71 PDFBibTeX XMLCite \textit{H. H. López} et al., Des. Codes Cryptography 89, No. 7, 1367--1403 (2021; Zbl 1469.13057) Full Text: DOI arXiv
Ghorpade, Sudhir R.; Singh, Prasant Pure resolutions, linear codes, and Betti numbers. (English) Zbl 1442.13038 J. Pure Appl. Algebra 224, No. 10, Article ID 106385, 21 p. (2020). MSC: 13D02 94B05 13F55 05B25 51E20 PDFBibTeX XMLCite \textit{S. R. Ghorpade} and \textit{P. Singh}, J. Pure Appl. Algebra 224, No. 10, Article ID 106385, 21 p. (2020; Zbl 1442.13038) Full Text: DOI arXiv
Ghorpade, Sudhir R. A note on Nullstellensatz over finite fields. (English) Zbl 1430.14054 Dani, Shrikrishna G. (ed.) et al., Contributions in algebra and algebraic geometry. International conference on algebra, discrete mathematics and applications, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, Maharashtra, India, December 9–11, 2017. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 738, 23-32 (2019). MSC: 14G15 11T06 13B25 11G25 14G05 PDFBibTeX XMLCite \textit{S. R. Ghorpade}, Contemp. Math. 738, 23--32 (2019; Zbl 1430.14054) Full Text: DOI arXiv
Martínez-Bernal, José; Pitones, Yuriko; Villarreal, Rafael H. Minimum distance functions of complete intersections. (English) Zbl 1404.13034 J. Algebra Appl. 17, No. 11, Article ID 1850204, 22 p. (2018). Reviewer: Steven T. Dougherty (Scranton) MSC: 13P25 94B60 11T71 PDFBibTeX XMLCite \textit{J. Martínez-Bernal} et al., J. Algebra Appl. 17, No. 11, Article ID 1850204, 22 p. (2018; Zbl 1404.13034) Full Text: DOI arXiv
Álvarez, Víctor; Armario, José Andrés; Falcón, Raúl M.; Frau, María Dolores; Gudiel, Félix Gröbner bases and cocyclic Hadamard matrices. (English) Zbl 1396.13024 J. Symb. Comput. 89, 26-40 (2018). MSC: 13P10 05B20 PDFBibTeX XMLCite \textit{V. Álvarez} et al., J. Symb. Comput. 89, 26--40 (2018; Zbl 1396.13024) Full Text: DOI arXiv
Tochimani, Azucena; Villarreal, Rafael H. Complete intersection vanishing ideals on sets of clutter type over finite fields. (English) Zbl 1391.14093 Bull. Malays. Math. Sci. Soc. (2) 41, No. 1, 81-89 (2018). Reviewer: Jebrel M. Habeb (Irbid) MSC: 14M10 14G15 13P25 13P10 11T71 PDFBibTeX XMLCite \textit{A. Tochimani} and \textit{R. H. Villarreal}, Bull. Malays. Math. Sci. Soc. (2) 41, No. 1, 81--89 (2018; Zbl 1391.14093) Full Text: DOI arXiv
Carvalho, Cícero; Neumann, Victor G. L. On the next-to-minimal weight of affine Cartesian codes. (English) Zbl 1354.14040 Finite Fields Appl. 44, 113-134 (2017). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 14G50 94B60 13P10 11T71 PDFBibTeX XMLCite \textit{C. Carvalho} and \textit{V. G. L. Neumann}, Finite Fields Appl. 44, 113--134 (2017; Zbl 1354.14040) Full Text: DOI
Tochimani, Azucena; Vaz Pinto, Maria; Villarreal, Rafael H. Direct products in projective Segre codes. (English) Zbl 1391.13059 Finite Fields Appl. 39, 96-110 (2016). Reviewer: Diego Ruano (Aalborg) MSC: 13P25 94B27 11T71 14N05 15A78 14G50 PDFBibTeX XMLCite \textit{A. Tochimani} et al., Finite Fields Appl. 39, 96--110 (2016; Zbl 1391.13059) Full Text: DOI arXiv
Neves, Jorge; Pinto, Maria Vaz; Villarreal, Rafael H. Vanishing ideals over graphs and even cycles. (English) Zbl 1314.13050 Commun. Algebra 43, No. 3, 1050-1075 (2015). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 13P25 14G50 14G15 94B27 PDFBibTeX XMLCite \textit{J. Neves} et al., Commun. Algebra 43, No. 3, 1050--1075 (2015; Zbl 1314.13050) Full Text: DOI arXiv
López, Hiram H.; Rentería-Márquez, Carlos; Villarreal, Rafael H. Affine Cartesian codes. (English) Zbl 1312.94118 Des. Codes Cryptography 71, No. 1, 5-19 (2014). Reviewer: Marco Calderini (Povo) MSC: 94B27 94B25 13P25 14G50 PDFBibTeX XMLCite \textit{H. H. López} et al., Des. Codes Cryptography 71, No. 1, 5--19 (2014; Zbl 1312.94118) Full Text: DOI arXiv
Vaz Pinto, Maria; Villarreal, Rafael H. The degree and regularity of vanishing ideals of algebraic toric sets over finite fields. (English) Zbl 1286.13022 Commun. Algebra 41, No. 9, 3376-3396 (2013). Reviewer: Yonglin Cao (Zibo) MSC: 13F20 13P10 11T71 94B25 PDFBibTeX XMLCite \textit{M. Vaz Pinto} and \textit{R. H. Villarreal}, Commun. Algebra 41, No. 9, 3376--3396 (2013; Zbl 1286.13022) Full Text: DOI arXiv
Sarmiento, Eliseo; Vaz Pinto, Maria; Villarreal, Rafael H. On the vanishing ideal of an algebraic toric set and its parametrized linear codes. (English) Zbl 1252.13019 J. Algebra Appl. 11, No. 4, Article ID 1250072, 16 p. (2012). Reviewer: David Joyner (Annapolis) MSC: 13P25 14G50 14G15 11T71 PDFBibTeX XMLCite \textit{E. Sarmiento} et al., J. Algebra Appl. 11, No. 4, Article ID 1250072, 16 p. (2012; Zbl 1252.13019) Full Text: DOI arXiv
Sarmiento, Eliseo; Vaz Pinto, Maria; Villarreal, Rafael H. The minimum distance of parameterized codes on projective tori. (English) Zbl 1271.13054 Appl. Algebra Eng. Commun. Comput. 22, No. 4, 249-264 (2011). Reviewer: Luis David Garcia Puente (Huntsville) MSC: 13P25 14G50 14G15 11T71 94B27 94B05 PDFBibTeX XMLCite \textit{E. Sarmiento} et al., Appl. Algebra Eng. Commun. Comput. 22, No. 4, 249--264 (2011; Zbl 1271.13054) Full Text: DOI arXiv
Rolland, Robert The second weight of generalized Reed-Muller codes in most cases. (English) Zbl 1192.94107 Cryptogr. Commun. 2, No. 1, 19-40 (2010). MSC: 94A60 13P10 PDFBibTeX XMLCite \textit{R. Rolland}, Cryptogr. Commun. 2, No. 1, 19--40 (2010; Zbl 1192.94107) Full Text: DOI arXiv
Cui, Jie; Wan, Zhexian On the dual of quaternary Goethals codes and their weight hierarchies. (English) Zbl 1099.94031 Sci. China, Ser. A 45, No. 11, 1361-1371 (2002). MSC: 94B05 11T71 13M10 PDFBibTeX XMLCite \textit{J. Cui} and \textit{Z. Wan}, Sci. China, Ser. A 45, No. 11, 1361--1371 (2002; Zbl 1099.94031) Full Text: DOI
Mercier, Dany-Jack; Rolland, Robert Homogeneous polynomials vanishing on the projective space \(\mathbb{P}^m(\mathbb{F}_q)\). (Polynômes homogènes qui s’annulent sur l’espace projectif \(\mathbb{P}^m(\mathbb{F}_q)\).) (French) Zbl 0899.13028 J. Pure Appl. Algebra 124, No. 1-3, 227-240 (1998). Reviewer: S.Balcerzyk (Toruń) MSC: 13M10 12E20 13C40 11T71 PDFBibTeX XMLCite \textit{D.-J. Mercier} and \textit{R. Rolland}, J. Pure Appl. Algebra 124, No. 1--3, 227--240 (1998; Zbl 0899.13028) Full Text: DOI
Rentería, C.; Tapia-Recillas, H. Reed-Muller codes: An ideal theory approach. (English) Zbl 0868.94045 Commun. Algebra 25, No. 2, 401-413 (1997). MSC: 94B05 13D25 13D40 PDFBibTeX XMLCite \textit{C. Rentería} and \textit{H. Tapia-Recillas}, Commun. Algebra 25, No. 2, 401--413 (1997; Zbl 0868.94045) Full Text: DOI