{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T03:52:52Z","timestamp":1775015572512,"version":"3.50.1"},"reference-count":37,"publisher":"Pleiades Publishing Ltd","issue":"2","license":[{"start":{"date-parts":[[2019,4,1]],"date-time":"2019-04-01T00:00:00Z","timestamp":1554076800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2019,4,1]],"date-time":"2019-04-01T00:00:00Z","timestamp":1554076800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Probl Inf Transm"],"published-print":{"date-parts":[[2019,4]]},"DOI":"10.1134\/s0032946019020029","type":"journal-article","created":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T07:03:40Z","timestamp":1562915020000},"page":"124-144","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Non-split Toric Codes"],"prefix":"10.1134","volume":"55","author":[{"given":"D. I.","family":"Koshelev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"137","published-online":{"date-parts":[[2019,7,12]]},"reference":[{"key":"4348_CR1","volume-title":"Advances in Algebraic Geometry Codes","year":"2008","unstructured":"Advances in Algebraic Geometry Codes, Mart\u00ednez-Moro, E., Munuera, C., and Ruano, D., Eds., Singapore: World Sci., 2008."},{"key":"4348_CR2","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/124","volume-title":"Toric Varieties","author":"DA Cox","year":"2011","unstructured":"Cox, D.A., Little, J.B., and Schenck, H.K., Toric Varieties, Providence, R.A.: Amer. Math. Soc., 2011."},{"key":"4348_CR3","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1007\/978-3-642-57189-3_12","volume-title":"Coding Theory, Cryptography and Related Areas","author":"JP Hansen","year":"2000","unstructured":"Hansen, J.P., Toric Surfaces and Error-Correcting Codes, Coding Theory, Cryptography and Related Areas (Proc. Int. Conf. on Coding Theory, Cryptography and Related Areas, held in Guanajuato, Mexico, in April 1998), Buchmann, J., H\u00f8holdt, T., Stichtenoth, H., and Tapia-Recillas, H., Eds., Berlin: Springer, 2000, pp. 132\u2013142."},{"issue":"4","key":"4348_CR4","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/s00200-002-0106-0","volume":"13","author":"JP Hansen","year":"2002","unstructured":"Hansen, J.P., Toric Varieties Hirzebruch Surfaces and Error-Correcting Codes, Appl. Algebra Engrg. Comm. Comput., 2002, vol. 13, no. 4, pp. 289\u2013300.","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"issue":"1","key":"4348_CR5","first-page":"31","volume":"3","author":"SD Berman","year":"1967","unstructured":"Berman, S.D., On the Theory of Group Codes, Kibernetika (Kiev), 1967, vol. 3, no. 1, pp. 31\u201339 [Cybernetics (Engl. Transl.), 1967, vol. 3, no. 1, pp. 25\u201331].","journal-title":"Kibernetika (Kiev)"},{"issue":"3","key":"4348_CR6","first-page":"21","volume":"3","author":"SD Berman","year":"1967","unstructured":"Berman, S.D., Semisimple Cyclic and Abelian Codes. II, Kibernetika (Kiev), 1967, vol. 3, no. 3, pp. 21\u201330 [Cybernetics (Engl. Transl.), 1967, vol. 3, no. 3, pp. 17\u201323].","journal-title":"Kibernetika (Kiev)"},{"issue":"1","key":"4348_CR7","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s00200-004-0152-x","volume":"15","author":"D Joyner","year":"2004","unstructured":"Joyner, D., Toric Codes over Finite Fields, Appl. Algebra Engrg. Comm. Comput., 2004, vol. 15, no. 1, pp. 63\u201379.","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"key":"4348_CR8","volume-title":"Algebraic Groups and Their Birational Invariants","author":"VE Voskresenskii","year":"1998","unstructured":"Voskresenskii, V.E., Algebraic Groups and Their Birational Invariants, Providence, R.A.: Amer. Math. Soc., 1998."},{"key":"4348_CR9","volume-title":"Algebrogeometricheskie kody. Osnovnye ponyatiya","author":"MA Tsfasman","year":"2003","unstructured":"Tsfasman, M.A., Vl\u0103du\u0163, S.G., and Nogin, D.Yu., Algebrogeometricheskie kody. Osnovnye ponyatiya, Moscow: MCCME, 2003. Translated under the title Algebraic Geometric Codes: Basic Notions, Providence, R.I.: Amer. Math. Soc., 2007."},{"issue":"3","key":"4348_CR10","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1016\/S0019-9958(64)90438-3","volume":"7","author":"JL Massey","year":"1964","unstructured":"Massey, J.L., Reversible Codes, Inform. Control, 1964, vol. 7, no. 3, pp. 369\u2013380.","journal-title":"Inform. Control"},{"issue":"2","key":"4348_CR11","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/0012-365X(90)90155-B","volume":"81","author":"G Lachaud","year":"1990","unstructured":"Lachaud, G., The Parameters of Projective Reed-M\u00fcller Codes, Discrete Math., 1990, vol. 81, no. 2, pp. 217\u2013221.","journal-title":"Discrete Math."},{"issue":"2","key":"4348_CR12","first-page":"195","volume":"46","author":"VE Voskresenskii","year":"1982","unstructured":"Voskresenskii, V.E., Projective Invariant Demazure Models, Izv. Akad. Nauk SSSR Ser. Mat., 1982, vol. 46, no. 2, pp. 195\u2013210 [Math. USSR Izv. (Engl. Transl.), 1983, vol. 20, no. 2, pp. 189\u2013202].","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"key":"4348_CR13","unstructured":"Grassl, M., Bounds on the Minimum Distance of Linear Codes and Quantum Codes (electronic tables). Available at http:\/\/www.codetables.de (accessed on October 12, 2018)."},{"key":"4348_CR14","volume-title":"Algebraicheskie gruppy i teoriya chisel","author":"VP Platonov","year":"1991","unstructured":"Platonov, V.P. and Rapinchuk, A.S., Algebraicheskie gruppy i teoriya chisel, Moscow: Nauka, 1991. Translated under the title Algebraic Groups and Number Theory, Boston: Academic, 1994."},{"issue":"5","key":"4348_CR15","doi-asserted-by":"publisher","first-page":"1401","DOI":"10.1137\/060676155","volume":"37","author":"K Rubin","year":"2008","unstructured":"Rubin, K. and Silverberg, A., Compression in Finite Fields and Torus-Based Cryptography, SIAM J. Comput., 2008, vol. 37, no. 5, pp. 1401\u20131428.","journal-title":"SIAM J. Comput."},{"issue":"1","key":"4348_CR16","first-page":"239","volume":"29","author":"VE Voskresenskii","year":"1965","unstructured":"Voskresenskii, V.E., On Two-Dimensional Algebraic Tori, Izv. Akad. Nauk SSSR Ser. Mat., 1965, vol. 29, no. 1, pp. 239\u2013244.","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"issue":"3","key":"4348_CR17","first-page":"711","volume":"31","author":"VE Voskresenskii","year":"1967","unstructured":"Voskresenskii, V.E., On Two-Dimensional Algebraic Tori. II, Izv. Akad. Nauk SSSR Ser. Mat., 1967, vol. 31, no. 3, pp. 711\u2013716 [Math. USSR Izv. (Engl. Transl.), 1967, vol. 1, no. 3, pp. 691\u2013696].","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"key":"4348_CR18","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1007\/978-3-642-18908-1_15","volume-title":"The Legacy of Niels Henrik Abel","author":"T Graber","year":"2004","unstructured":"Graber, T., Harris, J., Mazur, B., and Starr, J., Arithmetic Questions Related to Rationally Connected Varieties, The Legacy of Niels Henrik Abel (The Abel Bicentennial Conf., Oslo, Norway, June 3\u20138, 2002), Laudal, O.A., Ed., Berlin: Springer, 2004, pp. 531\u2013542."},{"issue":"2","key":"4348_CR19","first-page":"237","volume":"48","author":"VE Voskresenskii","year":"1984","unstructured":"Voskresenskii, V.E. and Klyachko, A.A., Toroidal Fano Varieties and Root Systems, Izv. Akad. Nauk SSSR Ser. Mat., 1984, vol. 48, no. 2, pp. 237\u2013263 [Math. USSR Izv. (Engl. Transl.), 1985, vol. 24, no. 2, pp. 221\u2013244].","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"issue":"2","key":"4348_CR20","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1155\/S1073792895000365","volume":"1995","author":"VV Batyrev","year":"1995","unstructured":"Batyrev, V.V. and Tschinkel, Y., Rational Points of Bounded Height on Compactifications of Anisotropic Tori, Int. Math. Res. Notices, 1995, vol. 1995, no. 2, pp. 591\u2013635.","journal-title":"Int. Math. Res. Notices"},{"key":"4348_CR21","unstructured":"Ballard, M.R., Duncan, A., and McFaddin, P.K., On Derived Categories of Arithmetic Toric Varieties, arXiv:1709.03574v3 [math.AG], 2018."},{"key":"4348_CR22","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/186","volume-title":"Rational Points on Varieties","author":"B Poonen","year":"2017","unstructured":"Poonen, B., Rational Points on Varieties, Providence, R.A.: Amer. Math. Soc., 2017."},{"key":"4348_CR23","volume-title":"Finite Projective Spaces of Three Dimensions","author":"JWP Hirschfeld","year":"1986","unstructured":"Hirschfeld, J.W.P., Finite Projective Spaces of Three Dimensions, Oxford: Oxford Univ. Press, 1986."},{"issue":"5","key":"4348_CR24","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1016\/j.ffa.2011.02.007","volume":"17","author":"A Couvreur","year":"2011","unstructured":"Couvreur, A., Construction of Rational Surfaces Yielding Good Codes, Finite Fields Appl., 2011, vol. 17, no. 5, pp. 424\u2013441.","journal-title":"Finite Fields Appl."},{"key":"4348_CR25","first-page":"92","volume-title":"Higher-Dimensional Geometry over Finite Fields","author":"J Koll\u00e1r","year":"2008","unstructured":"Koll\u00e1r, J., Looking for Rational Curves on Cubic Hypersurfaces, Higher-Dimensional Geometry over Finite Fields (Proc. of the NATO Advanced Study Institute, G\u00f6ttingen, Germany, June 25\u2013July 6, 2007), Kaledin, D. and Tschinkel Y., Eds., Amsterdam: IOS Press, 2008, pp. 92\u2013122."},{"key":"4348_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3849-0","volume-title":"Algebraic Geometry","author":"R Hartshorne","year":"1977","unstructured":"Hartshorne, R., Algebraic Geometry, Berlin: Springer, 1977. Translated under the title Algebraicheskaya geometriya, Moscow: Mir, 1981."},{"key":"4348_CR27","doi-asserted-by":"crossref","unstructured":"Hernando, F., O\u2019Sullivan, M.E., Popovici, E., and Srivastava, S., Subfield-Subcodes of Generalized Toric Codes, in Proc. 2010 IEEE Int. Sympos. on Information Theory (ISIT\u20192010), Austin, TX, USA, June 13\u201318, 2010, pp. 1125\u20131129.","DOI":"10.1109\/ISIT.2010.5513688"},{"key":"4348_CR28","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1016\/0012-365X(92)90563-U","volume":"106\u2013107","author":"JL Massey","year":"1992","unstructured":"Massey, J.L., Linear Codes with Complementary Duals, Discrete Math., 1992, vol. 106\u2013107, pp. 337\u2013342.","journal-title":"Discrete Math."},{"issue":"1\u20133","key":"4348_CR29","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1016\/0012-365X(94)90283-6","volume":"126","author":"X Yang","year":"1994","unstructured":"Yang, X. and Massey, J.L., The Condition for a Cyclic Code to Have a Complementary Dual, Discrete Math., 1994, vol. 126, no. 1\u20133, pp. 391\u2013393.","journal-title":"Discrete Math."},{"issue":"2","key":"4348_CR30","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1109\/TIT.1968.1054127","volume":"14","author":"T Kasami","year":"1968","unstructured":"Kasami, T., Lin, S., and Peterson, W., New Generalizations of the Reed-Muller Codes. I: Primitive Codes, IEEE Trans. Inform. Theory, 1968, vol. 14, no. 2, pp. 189\u2013199.","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"1\u20133","key":"4348_CR31","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/s10623-012-9692-4","volume":"66","author":"A Couvreur","year":"2013","unstructured":"Couvreur, A. and Duursma, I., Evaluation Codes from Smooth Quadric Surfaces and Twisted Segre Varieties, Des. Codes Cryptogr., 2013, vol. 66, no. 1\u20133, pp. 291\u2013303.","journal-title":"Des. Codes Cryptogr."},{"issue":"1","key":"4348_CR32","first-page":"18","volume":"34","author":"MI Boguslavsky","year":"1998","unstructured":"Boguslavsky, M.I., Sections of the Del Pezzo Surfaces and Generalized Weights, Probl. Peredachi Inf., 1998, vol. 34, no. 1, pp. 18\u201329 [Probl. Inf. Transm. (Engl. Transl.), 1998, vol. 34, no. 1, pp. 14\u201324].","journal-title":"Probl. Peredachi Inf."},{"issue":"4","key":"4348_CR33","doi-asserted-by":"publisher","first-page":"962","DOI":"10.1016\/j.ffa.2007.02.002","volume":"13","author":"D Ruano","year":"2007","unstructured":"Ruano, D., On the Parameters of r-Dimensional Toric Codes, Finite Fields Appl., 2007, vol. 13, no. 4, pp. 962\u2013976.","journal-title":"Finite Fields Appl."},{"key":"4348_CR34","first-page":"1","volume-title":"Arithmetic, Geometry and Coding Theory","author":"Y Aubry","year":"1996","unstructured":"Aubry, Y. and Perret, M., A Weil Theorem for Singular Curves, Arithmetic, Geometry and Coding Theory (Proc. Int. Conf. held at Luminy, France, June 28\u2013July 2, 1993), Pellikaan, R., Perret, M., and Vl\u0103du\u0163, S., Eds., Berlin: de Gruyter, 1996, pp. 1\u20137."},{"issue":"1","key":"4348_CR35","first-page":"59","volume":"38","author":"R Daskalov","year":"2002","unstructured":"Daskalov, R. and Hristov, P., New One-Generator Quasi-cyclic Codes over GF(7), Probl. Peredachi Inf., 2002, vol. 38, no. 1, pp. 59\u201363 [Probl. Inf. Transm. (Engl. Transl.), 2002, vol. 38, no. 1, pp. 50\u201354].","journal-title":"Probl. Peredachi Inf."},{"issue":"2","key":"4348_CR36","first-page":"29","volume":"39","author":"R Daskalov","year":"2003","unstructured":"Daskalov, R. and Hristov, P., New Quasi-cyclic Degenerate Linear Codes over GF(8), Probl. Peredachi Inf., 2003, vol. 39, no. 2, pp. 29\u201335 [Probl. Inf. Transm. (Engl. Transl.), 2003, vol. 39, no. 2, pp. 184\u2013190].","journal-title":"Probl. Peredachi Inf."},{"issue":"1","key":"4348_CR37","first-page":"15","volume":"40","author":"R Daskalov","year":"2004","unstructured":"Daskalov, R., Metodieva, E., and Hristov, P., New Minimum Distance Bounds for Linear Codes over GF(9), Probl. Peredachi Inf., 2004, vol. 40, no. 1, pp. 15\u201326 [Probl. Inf. Transm. (Engl. Transl.), 2004, vol. 40, no. 1, pp. 13\u201324].","journal-title":"Probl. Peredachi Inf."}],"container-title":["Problems of Information Transmission"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0032946019020029.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0032946019020029","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0032946019020029.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T02:29:03Z","timestamp":1775010543000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0032946019020029"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4]]},"references-count":37,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,4]]}},"alternative-id":["4348"],"URL":"https:\/\/doi.org\/10.1134\/s0032946019020029","relation":{},"ISSN":["0032-9460","1608-3253"],"issn-type":[{"value":"0032-9460","type":"print"},{"value":"1608-3253","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4]]},"assertion":[{"value":"22 November 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 January 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 January 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 July 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}