{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T14:04:32Z","timestamp":1766066672071,"version":"3.46.0"},"reference-count":25,"publisher":"Walter de Gruyter GmbH","issue":"3-4","license":[{"start":{"date-parts":[[2016,11,1]],"date-time":"2016-11-01T00:00:00Z","timestamp":1477958400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Two Boolean functions are affine equivalent if one can be obtained from the other by applying an affine transformation to the input variables. For a long time, there have been efforts to investigate the affine equivalence of Boolean functions. Due to the complexity of the general problem, only affine equivalence under certain groups of permutations is usually considered. Boolean functions which are invariant under the action of cyclic rotation of the input variables are known as rotation symmetric (RS) Boolean functions. Due to their speed of computation and the prospect of being good cryptographic Boolean functions, this class of Boolean functions has received a lot of attention from cryptographic researchers. In this paper, we study affine equivalence for the simplest rotation symmetric Boolean functions, called MRS functions, which are generated by the cyclic permutations of a single monomial. Using P\u00f3lya\u2019s enumeration theorem, we compute the number of equivalence classes, under certain large groups of permutations, for these MRS functions in any number\n                    <jats:italic>n<\/jats:italic>\n                    of variables. If\n                    <jats:italic>n<\/jats:italic>\n                    is prime, we obtain the number of equivalence classes under the group of all permutations of the variables.\n                  <\/jats:p>","DOI":"10.1515\/jmc-2016-0042","type":"journal-article","created":{"date-parts":[[2016,11,1]],"date-time":"2016-11-01T06:02:35Z","timestamp":1477980155000},"page":"145-156","source":"Crossref","is-referenced-by-count":6,"title":["Affine equivalence of monomial rotation symmetric Boolean functions: A P\u00f3lya\u2019s theorem approach"],"prefix":"10.1515","volume":"10","author":[{"given":"Thomas W.","family":"Cusick","sequence":"first","affiliation":[{"name":"Mathematics Department, University at Buffalo, Buffalo, NY 14260, United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K. V.","family":"Lakshmy","sequence":"additional","affiliation":[{"name":"TIFAC CORE in Cyber Security, Amrita School of Engineering, Coimbatore Amrita Vishwa Vidyapeetham, Amrita University, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Sethumadhavan","sequence":"additional","affiliation":[{"name":"TIFAC CORE in Cyber Security, Amrita School of Engineering, Coimbatore Amrita Vishwa Vidyapeetham, Amrita University, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,11,1]]},"reference":[{"key":"2025120600300291363_j_jmc-2016-0042_ref_001_w2aab3b7e1826b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"Berlekamp E. R. and Welch L. R.,\nWeight distributions of the cosets of the (32,6)${(32,6)}$ Reed\u2013Muller code,\nIEEE Trans. Inform. 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