{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T06:07:35Z","timestamp":1768975655368,"version":"3.49.0"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"3","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2015,3]]},"DOI":"10.1007\/s11075-014-9862-8","type":"journal-article","created":{"date-parts":[[2014,8,13]],"date-time":"2014-08-13T23:13:50Z","timestamp":1407971630000},"page":"585-600","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Fast algorithm for discrete fractional Hadamard transform"],"prefix":"10.1007","volume":"68","author":[{"given":"Aleksandr","family":"Cariow","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dorota","family":"Majorkowska-Mech","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,8,15]]},"reference":[{"key":"9862_CR1","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/S0030-4018(01)01462-6","volume":"197","author":"I\u015e Yetik","year":"2001","unstructured":"Yetik, I.\u015e., Kutay, M.A., Ozaktas, H.M.: Image representation and compression with the fractional Fourier transform. Opt. Commun. 197, 275\u2013278 (2001)","journal-title":"Opt. Commun."},{"key":"9862_CR2","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.optcom.2003.08.030","volume":"226","author":"B Hennelly","year":"2003","unstructured":"Hennelly, B., Sheridan, J.T.: Fractional Fourier transform-based image encryption: phase retrieval algorithm. Opt. Commun. 226, 61\u201380 (2003)","journal-title":"Opt. Commun."},{"key":"9862_CR3","doi-asserted-by":"crossref","first-page":"1242","DOI":"10.1364\/OL.26.001242","volume":"26","author":"S Liu","year":"2001","unstructured":"Liu, S., Mi, Q., Zhu, B.: Optical image encryption with multistage and multichannel fractional Fourier-domain filtering. Opt. Lett. 26, 1242\u20131244 (2001)","journal-title":"Opt. Lett."},{"key":"9862_CR4","doi-asserted-by":"crossref","first-page":"1583","DOI":"10.1117\/1.1570429","volume":"42","author":"NK Nischchal","year":"2003","unstructured":"Nischchal, N.K., Joseph, J., Singh, K.: Fully phase encryption using fractional Fourier transform. Opt. Eng. 42, 1583\u20131588 (2003)","journal-title":"Opt. Eng."},{"key":"9862_CR5","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1006\/jnca.2000.0128","volume":"24","author":"I Djurovi\u0107","year":"2001","unstructured":"Djurovi\u0107, I., Stankovi\u0107, S., Pitas, I.: Digital watermarking in the fractional Fourier transformation domain. J. Netw. Comput. Appl. 24, 167\u2013173 (2001)","journal-title":"J. Netw. Comput. Appl."},{"key":"9862_CR6","doi-asserted-by":"crossref","first-page":"1198","DOI":"10.1109\/78.923302","volume":"49","author":"SC Pei","year":"2001","unstructured":"Pei, S.C., Yeh, M.H.: The discrete fractional cosine and sine transforms. IEEE Trans. Sig. Proc. 49, 1198\u20131207 (2001)","journal-title":"IEEE Trans. Sig. Proc."},{"key":"9862_CR7","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1109\/82.686685","volume":"45","author":"SC Pei","year":"1998","unstructured":"Pei, S.C., Tseng, C.C., Yeh, M.H., Shyu, J.J.: The discrete fractional Hartley and Fourier transforms. IEEE Trans. Circuits Syst. Part II 45, 665\u2013675 (1998)","journal-title":"IEEE Trans. Circuits Syst. Part II"},{"key":"9862_CR8","doi-asserted-by":"crossref","unstructured":"Pei, S.C., Yeh, M.H., Shyu, J.J.: Discrete fractional Hadamard transform, Vol. 3, pp 179\u2013182 (1999)","DOI":"10.1109\/ISCAS.1999.778814"},{"key":"9862_CR9","first-page":"70","volume":"88","author":"D Majorkowska-Mech","year":"2012","unstructured":"Majorkowska-Mech, D., Cariow, A.: An algorithm for discrete fractional Hadamad transform with reduced arithmetical complexity. Przeglad Elektrotechniczny (Electrical Review) 88, 70\u201376 (2012)","journal-title":"Przeglad Elektrotechniczny (Electrical Review)"},{"key":"9862_CR10","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1080\/14786446708639914","volume":"34","author":"JJ Sylvester","year":"1867","unstructured":"Sylvester, J.J.: Thoughts on inverse orthogonal matrices, simultaneous sign-successions, and tessellated pavements in two or more colours, with applications to Newton\u2019s rule, ornamental tile-work, and the theory of numbers. Philos. Mag. 34, 461\u2013475 (1867)","journal-title":"Philos. Mag."},{"key":"9862_CR11","doi-asserted-by":"crossref","unstructured":"Bella, T., Olshevsky, V., Sankhnovich L: Ranks of Hadamard matrices and equivalence of Sylvester Hadamard and pseudo-noise matrices. Operator Theory: Advances and Applications, Vol. 179, pp 35\u201346. Birkhauser, Verlag, Basel\/Switzerland (2007)","DOI":"10.1007\/978-3-7643-8539-2_3"},{"key":"9862_CR12","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s11075-010-9422-9","volume":"57","author":"M Mitrouli","year":"2011","unstructured":"Mitrouli, M.: A sign test for detecting the equivalence of Sylvester Hadamard matrices. Numer. Algor. 57, 169\u2013186 (2011)","journal-title":"Numer. Algor."},{"key":"9862_CR13","volume-title":"Hadamard Matrices and their Applications","author":"KJ Horadam","year":"2006","unstructured":"Horadam, K.J.: Hadamard Matrices and their Applications. Princeton University Press, Princeton (2006)"},{"key":"9862_CR14","volume-title":"The Theory of Error-Correcting Codes","author":"NJA Sloane","year":"1977","unstructured":"Sloane, N.J.A., MacWilliams F.J.: The Theory of Error-Correcting Codes. Elsevier\/North-Holland, Amsterdam (1977)"},{"key":"9862_CR15","volume-title":"Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review","author":"GA Korn","year":"1968","unstructured":"Korn, G.A., Korn, T.M.: Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review. McGraw-Hill, New York (1968)"},{"key":"9862_CR16","doi-asserted-by":"crossref","first-page":"1329","DOI":"10.1109\/78.839980","volume":"48","author":"\u00c7C Candan","year":"2000","unstructured":"Candan, \u00c7.C., Kutay, M.A., Ozaktas, H.M.: The discrete fractional Fourier transform. IEEE Trans. Sig. Proc. 48, 1329\u20131337 (2000)","journal-title":"IEEE Trans. Sig. Proc."},{"key":"9862_CR17","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/0024-3795(82)90210-5","volume":"45","author":"R Yarlagadda","year":"1982","unstructured":"Yarlagadda, R., Hershey, J.: A note on the eigenvectors of Hadamard matrices of order 2 n . Linear Algebra Appl. 45, 43\u201353 (1982)","journal-title":"Linear Algebra Appl."},{"key":"9862_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-6313-6","volume-title":"Hadamard Matrix Analysis and Synthesis","author":"RKR Yarlagadda","year":"1997","unstructured":"Yarlagadda, R.K.R., Hershey, J.E: Hadamard Matrix Analysis and Synthesis. Kluwer Academic Publishers, Boston (1997)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-014-9862-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,4]],"date-time":"2025-05-04T05:30:44Z","timestamp":1746336644000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-014-9862-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8,15]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,3]]}},"alternative-id":["9862"],"URL":"https:\/\/doi.org\/10.1007\/s11075-014-9862-8","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8,15]]}}}