{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T05:06:08Z","timestamp":1738904768592,"version":"3.37.0"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,12,15]],"date-time":"2024-12-15T00:00:00Z","timestamp":1734220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,12,15]],"date-time":"2024-12-15T00:00:00Z","timestamp":1734220800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Hochschule Mannheim"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Theory Biosci."],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Circular codes, which are considered as putative remnants of primaeval comma-free codes, have recently become a focal point of research. These codes constitute a secondary type of genetic code, primarily tasked with detecting and preserving the normal reading frame within protein-coding sequences. The identification of a universal code present across various species has sparked numerous theoretical and experimental inquiries. Among these, the exploration of the class of 216 self-complementary <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$C^3$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>C<\/mml:mi>\n                    <mml:mn>3<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-codes of maximum size 20 has garnered significant attention. However, the origin of the number 216 lacks a satisfactory explanation, and the mathematical construction of these codes remains elusive. This paper introduces a new software designed to facilitate the construction of self-complementary <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$C^3$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>C<\/mml:mi>\n                    <mml:mn>3<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-codes (of maximum size). The approach involves a systematic exclusion of codons, guided by two fundamental mathematical theorems. These theorems demonstrate how codons can be automatically excluded from consideration when imposing requirements such as self-complementarity, circularity or maximality. By leveraging these theorems, our software provides a novel and efficient means to construct these intriguing circular codes, shedding light on their mathematical foundations and contributing to a deeper understanding of their biological significance.<\/jats:p>","DOI":"10.1007\/s12064-024-00431-6","type":"journal-article","created":{"date-parts":[[2024,12,15]],"date-time":"2024-12-15T18:59:17Z","timestamp":1734289157000},"page":"67-80","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Forbidden codon combinations in error-detecting circular codes"],"prefix":"10.1007","volume":"144","author":[{"given":"Elena","family":"Fimmel","sequence":"first","affiliation":[]},{"given":"Hadi","family":"Saleh","sequence":"additional","affiliation":[]},{"given":"Lutz","family":"Str\u00fcngmann","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,12,15]]},"reference":[{"issue":"7319","key":"431_CR1","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1038\/nature09534","volume":"467","author":"GR Abecasis","year":"2010","unstructured":"Abecasis GR, Altshuler D, Auton A, Brooks LD, Durbin RM, Gibbs RA et al (2010) A map of human genome variation from population-scale sequencing. 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