{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:38:25Z","timestamp":1787337505048,"version":"build-2736575974"},"reference-count":13,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:p>\n                    This paper shows that there is a connection between the crosscorrelation functions of certain binary m-sequences and the value sets of the polynomials x\n                    <jats:sup>k<\/jats:sup>\n                    (1 + x)\n                    <jats:sup>\n                      2\n                      <jats:sup>m<\/jats:sup>\n                      - 1\n                    <\/jats:sup>\n                    for k in pm 1, pm 2, 4, where x is in the finite field GF(2\n                    <jats:sup>2m<\/jats:sup>\n                    ). In particular, the size of such value sets is determined by using finite field theory and known results about crosscorrelation functions.\n                  <\/jats:p>","DOI":"10.1137\/s0097539794270352","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"120-131","source":"Crossref","is-referenced-by-count":5,"title":["Value Sets of Some Polynomials Over Finite Fields"],"prefix":"10.1137","volume":"27","author":[{"given":"Thomas W.","family":"Cusick","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,28]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.4064\/aa-5-4-417-423"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1952-09583-5"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.3792\/pjaa.68.338"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(76)90100-X"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(90)90013-3"},{"key":"R6","unstructured":"R. Lidl and H. Niederreiter,\n                      Finite Fields\n                      , Addison\u2013Wesley, Reading, MA, 1983."},{"key":"R7","unstructured":"Gary Mullen, Permutation polynomials over finite fields, Lecture Notes in Pure and Appl. Math., Vol. 141, Dekker, New York, 1993, 131\u201315194d:11097"},{"key":"R8","unstructured":"Y. Niho,\n                      Multi\u2010valued Cross\u2010correlation Functions Between Two Maximal Linear Recursive Sequences\n                      , Ph.D. thesis, USCEE Report 409, Dept. Elec. Eng., Univ. Southern California, Los Angeles, CA, 1972."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1980.11697"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.3792\/pja\/1195525873"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.4064\/aa-52-2-197-201"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700028860"},{"key":"R13","unstructured":"Da Wan, A p\u2010adic lifting lemma and its applications to permutation polynomials, Lecture Notes in Pure and Appl. Math., Vol. 141, Dekker, New York, 1993, 209\u201321693m:11129"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0097539794270352","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:14:33Z","timestamp":1787336073000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0097539794270352"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1137\/S0097539794270352"],"URL":"https:\/\/doi.org\/10.1137\/s0097539794270352","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}