{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T11:38:11Z","timestamp":1778931491962,"version":"3.51.4"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,3,12]],"date-time":"2018-03-12T00:00:00Z","timestamp":1520812800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Theory Biosci."],"published-print":{"date-parts":[[2018,4]]},"DOI":"10.1007\/s12064-018-0259-4","type":"journal-article","created":{"date-parts":[[2018,3,12]],"date-time":"2018-03-12T02:56:39Z","timestamp":1520823399000},"page":"51-65","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Self-complementary circular codes in coding theory"],"prefix":"10.1007","volume":"137","author":[{"given":"Elena","family":"Fimmel","sequence":"first","affiliation":[]},{"given":"Christian J.","family":"Michel","sequence":"additional","affiliation":[]},{"given":"Martin","family":"Starman","sequence":"additional","affiliation":[]},{"given":"Lutz","family":"Str\u00fcngmann","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,3,12]]},"reference":[{"key":"259_CR1","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1006\/jtbi.1996.0142","volume":"182","author":"DG Arqu\u00e8s","year":"1996","unstructured":"Arqu\u00e8s DG, Michel CJ (1996) A complementary circular code in the protein coding genes. J Theor Biol 182:45\u201358","journal-title":"J Theor Biol"},{"key":"259_CR2","doi-asserted-by":"publisher","DOI":"10.1142\/1280","volume-title":"A first look at graph theory","author":"J Clark","year":"1991","unstructured":"Clark J, Holton DA (1991) A first look at graph theory. World Scientific, New Jersey"},{"key":"259_CR3","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/BF00927934","volume":"7","author":"FH Crick","year":"1976","unstructured":"Crick FH, Brenner S, Klug A, Pieczenik G (1976) A speculation on the origin of protein synthesis. Orig Life 7:389\u2013397","journal-title":"Orig Life"},{"key":"259_CR4","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1073\/pnas.43.5.416","volume":"43","author":"FH Crick","year":"1957","unstructured":"Crick FH, Griffith JS, Orgel LE (1957) Codes without commas. Proc Natl Acad Sci USA 43:416\u2013421","journal-title":"Proc Natl Acad Sci USA"},{"key":"259_CR5","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/BF00439699","volume":"65","author":"M Eigen","year":"1978","unstructured":"Eigen M, Schuster P (1978) The hypercycle. A principle of natural self-organization. Part C: The realistic hypercycle. Naturwissenschaften 65:341\u2013369","journal-title":"Naturwissenschaften"},{"key":"259_CR6","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/j.compbiolchem.2014.08.001","volume":"52","author":"K Soufi El","year":"2014","unstructured":"El Soufi K, Michel CJ (2014) Circular code motifs in the ribosome decoding center. Comput Biol Chem 52:9\u201317","journal-title":"Comput Biol Chem"},{"key":"259_CR7","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1016\/j.compbiolchem.2015.07.015","volume":"59","author":"K Soufi El","year":"2015","unstructured":"El Soufi K, Michel CJ (2015) Circular code motifs near the ribosome decoding center. Comput Biol Chem 59:158\u2013176","journal-title":"Comput Biol Chem"},{"key":"259_CR8","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1016\/j.jtbi.2016.07.022","volume":"408","author":"K Soufi El","year":"2016","unstructured":"El Soufi K, Michel CJ (2016) Circular code motifs in genomes of eukaryotes. J Theor Biol 408:198\u2013212","journal-title":"J Theor Biol"},{"key":"259_CR9","doi-asserted-by":"publisher","first-page":"20150058","DOI":"10.1098\/rsta.2015.0058","volume":"374","author":"E Fimmel","year":"2016","unstructured":"Fimmel E, Michel CJ, Str\u00fcngmann L (2016) \n                    \n                      \n                    \n                    $$n$$\n                    \n                      \n                        n\n                      \n                    \n                  -Nucleotide circular codes in graph theory. Philos Trans R Soc A 374:20150058","journal-title":"Philos Trans R Soc A"},{"key":"259_CR10","doi-asserted-by":"publisher","first-page":"1796","DOI":"10.1007\/s11538-017-0307-0","volume":"79","author":"E Fimmel","year":"2017","unstructured":"Fimmel E, Michel CJ, Str\u00fcngmann L (2017) Strong comma-free codes in genetic information. Bull Math Biol 79:1796\u20131819","journal-title":"Bull Math Biol"},{"key":"259_CR11","first-page":"1","volume":"23","author":"SW Golomb","year":"1958","unstructured":"Golomb SW, Delbruck M, Welch LR (1958a) Construction and properties of comma-free codes. Biol Medd K Dan Vidensk Selsk 23:1\u201334","journal-title":"Biol Medd K Dan Vidensk Selsk"},{"key":"259_CR12","doi-asserted-by":"publisher","first-page":"202","DOI":"10.4153\/CJM-1958-023-9","volume":"10","author":"SW Golomb","year":"1958","unstructured":"Golomb SW, Gordon B, Welch LR (1958b) Comma-free codes. Can J Math 10:202\u2013209","journal-title":"Can J Math"},{"key":"259_CR13","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1007\/BF02703773","volume":"27","author":"K Ikehara","year":"2002","unstructured":"Ikehara K (2002) Origins of gene, genetic code, protein and life: comprehensive view of life systems from a GNC-SNS primitive genetic code hypothesis. J Biosci 27:165\u2013186","journal-title":"J Biosci"},{"key":"259_CR14","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/j.compbiolchem.2011.10.002","volume":"37","author":"CJ Michel","year":"2012","unstructured":"Michel CJ (2012) Circular code motifs in transfer and 16S ribosomal RNAs: a possible translation code in genes. Comput Biol Chem 37:24\u201337","journal-title":"Comput Biol Chem"},{"key":"259_CR15","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.compbiolchem.2013.02.004","volume":"45","author":"CJ Michel","year":"2013","unstructured":"Michel CJ (2013) Circular code motifs in transfer RNAs. Comput Biol Chem 45:17\u201329","journal-title":"Comput Biol Chem"},{"key":"259_CR16","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1016\/j.jtbi.2015.04.009","volume":"380","author":"CJ Michel","year":"2015","unstructured":"Michel CJ (2015) The maximal \n                    \n                      \n                    \n                    $$C^3$$\n                    \n                      \n                        \n                          C\n                          3\n                        \n                      \n                    \n                   self-complementary trinucleotide circular code \n                    \n                      \n                    \n                    $$X$$\n                    \n                      \n                        X\n                      \n                    \n                   in genes of bacteria, eukaryotes, plasmids and viruses. J Theor Biol 380:156\u2013177","journal-title":"J Theor Biol"},{"issue":"20","key":"259_CR17","first-page":"1","volume":"7","author":"CJ Michel","year":"2017","unstructured":"Michel CJ (2017) The maximal \n                    \n                      \n                    \n                    $$C^3$$\n                    \n                      \n                        \n                          C\n                          3\n                        \n                      \n                    \n                   self-complementary trinucleotide circular code \n                    \n                      \n                    \n                    $$X$$\n                    \n                      \n                        X\n                      \n                    \n                   in genes of bacteria, archaea, eukaryotes, plasmids and viruses. Life 7(20):1\u201316","journal-title":"Life"},{"issue":"52","key":"259_CR18","first-page":"1","volume":"7","author":"CJ Michel","year":"2017","unstructured":"Michel CJ, Nguefack Ngoune V, Poch O, Ripp R, Thompson JD (2017) Enrichment of circular code motifs in the genes of the yeast Saccharomyces cerevisiae. Life 7(52):1\u201320","journal-title":"Life"},{"key":"259_CR19","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1016\/j.camwa.2006.12.091","volume":"55","author":"CJ Michel","year":"2008","unstructured":"Michel CJ, Pirillo G, Pirillo MA (2008) Varieties of comma free codes. Comput Math Appl 55:989\u2013996","journal-title":"Comput Math Appl"},{"key":"259_CR20","doi-asserted-by":"publisher","first-page":"1596","DOI":"10.1073\/pnas.78.3.1596","volume":"78","author":"JCW Shepherd","year":"1981","unstructured":"Shepherd JCW (1981) Method to determine the reading frame of a protein from the purine\/pyrimidine genome sequence and its possible evolutionary justification. Proc Natl Acad Sci USA 78:1596\u20131600","journal-title":"Proc Natl Acad Sci USA"},{"key":"259_CR21","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1016\/0022-2836(87)90241-5","volume":"194","author":"EN Trifonov","year":"1987","unstructured":"Trifonov EN (1987) Translation framing code and frame-monitoring mechanism as suggested by the analysis of mRNA and 16S rRNA nucleotide sequences. J Mol Biol 194:643\u2013652","journal-title":"J Mol Biol"}],"container-title":["Theory in Biosciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12064-018-0259-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12064-018-0259-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12064-018-0259-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,11]],"date-time":"2019-03-11T20:59:45Z","timestamp":1552337985000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12064-018-0259-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,12]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,4]]}},"alternative-id":["259"],"URL":"https:\/\/doi.org\/10.1007\/s12064-018-0259-4","relation":{},"ISSN":["1431-7613","1611-7530"],"issn-type":[{"value":"1431-7613","type":"print"},{"value":"1611-7530","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,12]]},"assertion":[{"value":"11 July 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 February 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 March 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}