{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:26:26Z","timestamp":1772119586104,"version":"3.50.1"},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T00:00:00Z","timestamp":1718150400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T00:00:00Z","timestamp":1718150400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"GNSAGA-INDAM"},{"DOI":"10.13039\/501100010607","name":"Universit\u00e0 degli Studi di Perugia","doi-asserted-by":"publisher","award":["98751"],"award-info":[{"award-number":["98751"]}],"id":[{"id":"10.13039\/501100010607","id-type":"DOI","asserted-by":"publisher"}]},{"name":"OSINT","award":["2021"],"award-info":[{"award-number":["2021"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2024,11]]},"DOI":"10.1007\/s10623-024-01438-2","type":"journal-article","created":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T09:03:57Z","timestamp":1718183037000},"page":"3371-3375","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An asymptotic property of quaternary additive codes"],"prefix":"10.1007","volume":"92","author":[{"given":"J\u00fcrgen","family":"Bierbrauer","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7961-0260","authenticated-orcid":false,"given":"Stefano","family":"Marcugini","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5476-5365","authenticated-orcid":false,"given":"Fernanda","family":"Pambianco","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,12]]},"reference":[{"key":"1438_CR1","volume-title":"Introduction to Coding Theory","author":"J Bierbrauer","year":"2017","unstructured":"Bierbrauer J.: Introduction to Coding Theory, 2nd edn Chapman and Hall\/CRC Press, Boca Raton (2017).","edition":"2"},{"key":"1438_CR2","doi-asserted-by":"publisher","first-page":"5116","DOI":"10.1109\/TIT.2021.3085577","volume":"67","author":"J Bierbrauer","year":"2021","unstructured":"Bierbrauer J., Marcugini S., Pambianco F.: Optimal additive quaternary codes of low dimension. IEEE IT Trans. 67, 5116\u20135118 (2021).","journal-title":"IEEE IT Trans."},{"key":"1438_CR3","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/S0195-6698(03)00096-9","volume":"25","author":"A Blokhuis","year":"2004","unstructured":"Blokhuis A., Brouwer A.E.: Small additive quaternary codes. Eur. J. Combin. 25, 161\u2013167 (2004).","journal-title":"Eur. J. Combin."},{"key":"1438_CR4","doi-asserted-by":"publisher","first-page":"53","DOI":"10.2140\/iig.2008.6.53","volume":"6","author":"J Bierbrauer","year":"2009","unstructured":"Bierbrauer J., Faina G., Giulietti M., Marcugini S., Pambianco F.: The geometry of quantum codes. Innov. Incidence Geom. 6, 53\u201371 (2009).","journal-title":"Innov. Incidence Geom."},{"key":"1438_CR5","doi-asserted-by":"publisher","first-page":"1369","DOI":"10.1109\/18.681315","volume":"44","author":"AR Calderbank","year":"1998","unstructured":"Calderbank A.R., Rains E.M., Shor P.M., Sloane N.J.A.: Quantum error-correction via codes over $$GF(4)$$. IEEE Trans. Inf. Theory 44, 1369\u20131387 (1998).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1438_CR6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.81.022322","volume":"81","author":"Y Dong","year":"2010","unstructured":"Dong Y., Hu D., Yu S.: Breeding quantum error-correcting codes. Phys. Rev. A 81, 022322 (2010).","journal-title":"Phys. Rev. A"},{"key":"1438_CR7","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/s10623-015-0156-5","volume":"78","author":"T Etzion","year":"2016","unstructured":"Etzion T., Storme L.: Galois geometries and coding theory. Des. Codes Cryptogr. 78, 311\u2013350 (2016).","journal-title":"Des. Codes Cryptogr."},{"key":"1438_CR8","series-title":"London Math. Soc., Lecture Notes Series","first-page":"51","volume-title":"Surveys in Combinatorics","author":"M Giulietti","year":"2013","unstructured":"Giulietti M.: The geometry of covering codes: small complete caps and saturating sets in Galois spaces. In: Blackburn S.R., Holloway R., Wildon M. (eds.) Surveys in Combinatorics, vol. 409, pp. 51\u201390. London Math. Soc., Lecture Notes Series. Cambridge University Press, Cambridge (2013)."},{"key":"1438_CR9","doi-asserted-by":"publisher","first-page":"03013","DOI":"10.1051\/itmconf\/20171203013","volume":"12","author":"LB Guo","year":"2017","unstructured":"Guo L.B., Liu Y., Lu L.D., Li R.H.: On construction of good quaternary additive codes. ITM Web Sci. 12, 03013 (2017).","journal-title":"ITM Web Sci."},{"key":"1438_CR10","volume-title":"Finite Projective Spaces of Three Dimensions","author":"JWP Hirschfeld","year":"1985","unstructured":"Hirschfeld J.W.P.: Finite Projective Spaces of Three Dimensions. Oxford University Press, Oxford (1985)."},{"key":"1438_CR11","volume-title":"Projective Geometries Over Finite Fields","author":"JWP Hirschfeld","year":"1999","unstructured":"Hirschfeld J.W.P.: Projective Geometries Over Finite Fields, 2nd edn Oxford University Press, Oxford (1999).","edition":"2"},{"key":"1438_CR12","doi-asserted-by":"crossref","unstructured":"Hirschfeld J.W.P., Storme L.: The packing problem in statistics, coding theory and finite projective spaces: Update 2001. Finite Geometries (Proc. 4th Isle of Thorns Conf., July 16-21, 2000), eds. Blokhuis A., Hirschfeld J.W.P., Jungnickel D., Thas J.A., Develop. Math., 3, Kluwer, Dordrecht, 201-246 (2001)","DOI":"10.1007\/978-1-4613-0283-4_13"},{"key":"1438_CR13","first-page":"187","volume-title":"Current Research Topics in Galois Geometry","author":"I Landjev","year":"2011","unstructured":"Landjev I., Storme L.: Galois geometry and coding theory. In: De Beule J., Storme L. (eds.) Current Research Topics in Galois Geometry, vol. 31, pp. 187\u2013214. NOVA Academic, New York (2011)."},{"key":"1438_CR14","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/s10623-022-01106-3","volume":"91","author":"M Shi","year":"2023","unstructured":"Shi M., Liu L., Kim J.L., Sol\u00e9 P.: Additive complementary dual codes over $$GF(4),$$. Des. Codes Cryptogr. 91, 273\u2013284 (2023).","journal-title":"Des. Codes Cryptogr."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-024-01438-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-024-01438-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-024-01438-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,29]],"date-time":"2024-09-29T14:02:41Z","timestamp":1727618561000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-024-01438-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,12]]},"references-count":14,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2024,11]]}},"alternative-id":["1438"],"URL":"https:\/\/doi.org\/10.1007\/s10623-024-01438-2","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-3255586\/v1","asserted-by":"object"}]},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,12]]},"assertion":[{"value":"19 October 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 January 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 May 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 June 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"On behalf of all authors, the corresponding author states that there is no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}