{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T10:45:14Z","timestamp":1725533114009},"publisher-location":"Berlin, Heidelberg","reference-count":17,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642021800"},{"type":"electronic","value":"9783642021817"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-642-02181-7_5","type":"book-chapter","created":{"date-parts":[[2009,6,6]],"date-time":"2009-06-06T01:43:20Z","timestamp":1244252600000},"page":"43-52","source":"Crossref","is-referenced-by-count":0,"title":["Rank for Some Families of Quaternary Reed-Muller Codes"],"prefix":"10.1007","author":[{"given":"Jaume","family":"Pernas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaume","family":"Pujol","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Merc\u00e8","family":"Villanueva","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"5_CR1","volume-title":"Introduction to coding theory","author":"J. Bierbrauer","year":"2005","unstructured":"Bierbrauer, J.: Introduction to coding theory. Chapman & Hall\/CRC, Boca Raton (2005)"},{"issue":"7","key":"5_CR2","doi-asserted-by":"publisher","first-page":"2686","DOI":"10.1109\/TIT.2005.850148","volume":"51","author":"J. Borges","year":"2005","unstructured":"Borges, J., Fern\u00e1ndez, C., Phelps, K.T.: Quaternary Reed-Muller codes. IEEE Trans. Inform. Theory\u00a051(7), 2686\u20132691 (2005)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"1","key":"5_CR3","doi-asserted-by":"publisher","first-page":"380","DOI":"10.1109\/TIT.2007.911211","volume":"54","author":"J. Borges","year":"2008","unstructured":"Borges, J., Fern\u00e1ndez-C\u00f3rdoba, C., Phelps, K.T.: \u201cZRM codes\u201d. IEEE Trans. Inform. Theory\u00a054(1), 380\u2013386 (2008)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"11","key":"5_CR4","doi-asserted-by":"publisher","first-page":"2834","DOI":"10.1109\/TIT.2003.819329","volume":"49","author":"J. Borges","year":"2003","unstructured":"Borges, J., Phelps, K.T., Rif\u00e0, J., Zinoviev, V.A.: On Z\n                  4-linear Preparata-like and Kerdock-like codes. IEEE Trans. Inform. Theory\u00a049(11), 2834\u20132843 (2003)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"8","key":"5_CR5","doi-asserted-by":"publisher","first-page":"2028","DOI":"10.1109\/TIT.2003.814490","volume":"49","author":"J. Borges","year":"2003","unstructured":"Borges, J., Phelps, K.T., Rif\u00e0, J.: The rank and kernel of extended 1-perfect Z\n                  4-linear and additive non-Z\n                  4-linear codes. IEEE Trans. Inform. Theory\u00a049(8), 2028\u20132034 (2003)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"5_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1007\/978-3-540-87448-5_6","volume-title":"Coding Theory and Applications","author":"C. Fern\u00e1ndez-C\u00f3rdoba","year":"2008","unstructured":"Fern\u00e1ndez-C\u00f3rdoba, C., Pujol, J., Villanueva, M.: On rank and kernel of Z\n                  4-linear codes. In: Barbero, A. (ed.) ICMCTA 2008. LNCS, vol.\u00a05228, pp. 46\u201355. Springer, Heidelberg (2008)"},{"key":"5_CR7","unstructured":"Fern\u00e1ndez-C\u00f3rdoba, C., Pujol, J., Villanueva, M.: \u21242\u21244-linear codes: rank and kernel. Discrete Applied Mathematics (2008) (submitted), arXiv:0807.4247"},{"key":"5_CR8","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1109\/18.312154","volume":"40","author":"A.R. Hammons","year":"1994","unstructured":"Hammons, A.R., Kumar, P.V., Calderbank, A.R., Sloane, N.J.A., Sol\u00e9, P.: The Z\n                  4-linearity of Kerdock, Preparata, Goethals and related codes. IEEE Trans. Inform. Theory\u00a040, 301\u2013319 (1994)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"5_CR9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511807077","volume-title":"Fundamentals of Error-Correcting Codes","author":"W.C. Huffman","year":"2003","unstructured":"Huffman, W.C., Pless, V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2003)"},{"key":"5_CR10","doi-asserted-by":"crossref","unstructured":"Krotov, D.S.: Z\n                  4-linear Hadamard and extended perfect codes. In: International Workshop on Coding and Cryptography, Paris, France, January 8-12, pp. 329\u2013334 (2001)","DOI":"10.1016\/S1571-0653(04)00161-1"},{"key":"5_CR11","volume-title":"The Theory of Error-Correcting Codes","author":"F.J. MacWilliams","year":"1977","unstructured":"MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland Publishing Company, Amsterdam (1977)"},{"issue":"1","key":"5_CR12","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1109\/TIT.2005.860464","volume":"52","author":"K.T. Phelps","year":"2006","unstructured":"Phelps, K.T., Rif\u00e0, J., Villanueva, M.: On the additive (Z\n                  4-linear and non-Z\n                  4-linear) Hadamard codes: rank and kernel. IEEE Trans. Inform. Theory\u00a052(1), 316\u2013319 (2006)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"5_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1007\/978-3-540-89994-5_11","volume-title":"Beth Festschrift","author":"J. Pernas","year":"2008","unstructured":"Pernas, J., Pujol, J., Villanueva, M.: Kernel dimension for some families of quaternary Reed-Muller codes. In: Calmet, J., Geiselmann, W., M\u00fcller-Quade, J. (eds.) Beth Festschrift. LNCS, vol.\u00a05393, pp. 128\u2013141. Springer, Heidelberg (2008)"},{"key":"5_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1007\/978-3-540-77224-8_19","volume-title":"Applied Algebra, Algebraic Algorithms and Error-Correcting Codes","author":"J. Pujol","year":"2007","unstructured":"Pujol, J., Rif\u00e0, J., Solov\u2019eva, F.I.: Quaternary Plotkin constructions and quaternary Reed-Muller codes. In: Bozta\u015f, S., Lu, H.-F(F.) (eds.) AAECC 2007. LNCS, vol.\u00a04851, pp. 148\u2013157. Springer, Heidelberg (2007)"},{"issue":"1","key":"5_CR15","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1109\/TIT.2008.2008143","volume":"55","author":"J. Pujol","year":"2009","unstructured":"Pujol, J., Rif\u00e0, J., Solov\u00e9va, F.I.: Construction of Z\n                  4-linear Reed-Muller codes. IEEE Trans. Inform. Theory\u00a055(1), 99\u2013104 (2009)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"1","key":"5_CR16","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1134\/S0032946007010048","volume":"43","author":"F.I. Solov\u2019eva","year":"2007","unstructured":"Solov\u2019eva, F.I.: On Z4-linear codes with parameters of Reed-Muller codes. Problems of Inform. Trans.\u00a043(1), 26\u201332 (2007)","journal-title":"Problems of Inform. Trans."},{"key":"5_CR17","doi-asserted-by":"publisher","DOI":"10.1142\/3603","volume-title":"Quaternary codes","author":"Z.-X. Wan","year":"1997","unstructured":"Wan, Z.-X.: Quaternary codes. World Scientific Publishing Co. Pte. Ltd., Singapore (1997)"}],"container-title":["Lecture Notes in Computer Science","Applied Algebra, Algebraic Algorithms and Error-Correcting Codes"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-02181-7_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,8]],"date-time":"2019-03-08T18:24:50Z","timestamp":1552069490000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-02181-7_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783642021800","9783642021817"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-02181-7_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2009]]}}}