{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T17:31:16Z","timestamp":1782322276698,"version":"3.54.5"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2023,1,10]],"date-time":"2023-01-10T00:00:00Z","timestamp":1673308800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,10]],"date-time":"2023-01-10T00:00:00Z","timestamp":1673308800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2023,5]]},"DOI":"10.1007\/s10623-022-01176-3","type":"journal-article","created":{"date-parts":[[2023,1,10]],"date-time":"2023-01-10T12:02:49Z","timestamp":1673352169000},"page":"1737-1750","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A general family of Plotkin-optimal two-weight codes over $$\\mathbb {Z}_4$$"],"prefix":"10.1007","volume":"91","author":[{"given":"Hopein Christofen","family":"Tang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2836-9358","authenticated-orcid":false,"given":"Djoko","family":"Suprijanto","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,1,10]]},"reference":[{"issue":"2","key":"1176_CR1","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1112\/jlms\/s2-26.2.365","volume":"26","author":"R Calderbank","year":"1982","unstructured":"Calderbank R.: On uniformly packed $$[n, n-k,4]$$ codes over $$GF(q)$$ and a class of caps in $$PG(k-1, q),$$. J. Lond. Math. Soc. 26(2), 365\u2013384 (1982).","journal-title":"J. Lond. Math. Soc."},{"key":"1176_CR2","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1112\/blms\/18.2.97","volume":"18","author":"R Calderbank","year":"1986","unstructured":"Calderbank R., Kantor W.M.: The geometry of two-weight codes. Bull. Lond. Math. Soc. 18, 97\u2013122 (1986).","journal-title":"Bull. Lond. Math. Soc."},{"key":"1176_CR3","volume-title":"Coding Theory, Cryptography and Related Areas","author":"C Carlet","year":"2000","unstructured":"Carlet C.: One-weight $${\\mathbb{Z} }$$-linear codes. In: Buchmann J., et al. (eds.) Coding Theory, Cryptography and Related Areas. Springer, New York (2000)."},{"key":"1176_CR4","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/0012-365X(72)90024-6","volume":"3","author":"P Delsarte","year":"1972","unstructured":"Delsarte P.: Weights of linear codes and strongly regular normed spaces. Discret Math. 3, 47\u201362 (1972).","journal-title":"Discret Math."},{"issue":"2","key":"1176_CR5","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1109\/18.312154","volume":"40","author":"AR Hammons","year":"1994","unstructured":"Hammons A.R., Kumar P.V., Calderbank A.R., Sloane N.J.A., Sol\u00e9 P.: The $${\\mathbb{Z} }_4$$-linearity of Kerdock, Preparata, Goethals and related codes. IEEE Trans. Inform. Theory 40(2), 301\u2013319 (1994).","journal-title":"IEEE Trans. Inform. Theory"},{"key":"1176_CR6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511807077","volume-title":"Fundamentals of Error Correcting Codes","author":"WC Huffman","year":"2003","unstructured":"Huffman W.C., Pless V.: Fundamentals of Error Correcting Codes. Cambridge University Press, Cambridge (2003)."},{"key":"1176_CR7","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1016\/0012-365X(92)90559-X","volume":"106\u2013107","author":"T Kl\u00f8ve","year":"1992","unstructured":"Kl\u00f8ve T.: Support weight distribution of linear codes. Discret Math. 106\u2013107, 311\u2013316 (1992).","journal-title":"Discret Math."},{"key":"1176_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/s12190-022-01736-9","author":"S Li","year":"2022","unstructured":"Li S., Shi M.: Two infinite families of two-weight codes over $${\\mathbb{Z} }_{2^m}$$. J. Appl. Math. Comput. (2022). https:\/\/doi.org\/10.1007\/s12190-022-01736-9.","journal-title":"J. Appl. Math. Comput."},{"key":"1176_CR9","volume-title":"The Theory of Error-Correcting Codes","author":"FJ MacWilliams","year":"1977","unstructured":"MacWilliams F.J., Sloane N.J.A.: The Theory of Error-Correcting Codes. North-Holland Publishing Company, Amsterdam (1977)."},{"issue":"10","key":"1176_CR10","doi-asserted-by":"publisher","first-page":"6240","DOI":"10.1109\/TIT.2017.2742499","volume":"63","author":"M Shi","year":"2017","unstructured":"Shi M., Guan Y., Sol\u00e9 P.: Two new families of two-weight codes. IEEE Trans. Inf. Theory 63(10), 6240\u20136246 (2017).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"12","key":"1176_CR11","doi-asserted-by":"publisher","first-page":"7769","DOI":"10.1109\/TIT.2021.3114636","volume":"67","author":"M Shi","year":"2021","unstructured":"Shi M., Honold T., Sol\u00e9 P., Qiu Y., Wu R., Sepasdar Z.: The geometry of two-weight codes over $${\\mathbb{Z} }_{p^m}$$. IEEE Trans. Inf. Theory 67(12), 7769\u20137781 (2021).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"1176_CR12","doi-asserted-by":"publisher","first-page":"1201","DOI":"10.1007\/s10623-017-0390-0","volume":"86","author":"M Shi","year":"2018","unstructured":"Shi M., Sepasdar Z., Alahmadi A., Sol\u00e9 P.: On two-weight $${\\mathbb{Z} }_{2^k}$$-codes. Des. Codes Cryptogr. 86(6), 1201\u20131209 (2018).","journal-title":"Des. Codes Cryptogr."},{"issue":"4","key":"1176_CR13","doi-asserted-by":"publisher","first-page":"795","DOI":"10.1007\/s11424-014-2188-8","volume":"27","author":"M Shi","year":"2014","unstructured":"Shi M., Wang Y.: Optimal binary codes from one-Lee weight codes and two-Lee weight projective codes over $${\\mathbb{Z} }_4,$$. J. Syst. Sci. Complex. 27(4), 795\u2013810 (2014).","journal-title":"J. Syst. Sci. Complex."},{"issue":"1","key":"1176_CR14","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1109\/TIT.2016.2628408","volume":"63","author":"M Shi","year":"2017","unstructured":"Shi M., Xu L.L., Yang G.: A note on one weight and two weight projective $${\\mathbb{Z} }_4$$-codes. IEEE Trans. Inf. Theory 63(1), 177\u2013182 (2017).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"12","key":"1176_CR15","doi-asserted-by":"publisher","first-page":"2493","DOI":"10.1007\/s10623-020-00796-x","volume":"88","author":"M Shi","year":"2020","unstructured":"Shi M., Xuan W., Sol\u00e9 P.: Two families of two-weight codes over $${\\mathbb{Z} }_4$$. Des. Codes Cryptogr. 88(12), 2493\u20132505 (2020).","journal-title":"Des. Codes Cryptogr."},{"key":"1176_CR16","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972722000399","author":"HC Tang","year":"2022","unstructured":"Tang H.C., Suprijanto D.: New optimal linear codes over $${\\mathbb{Z} }_4$$. Bull. Aust. Math. Soc. (2022). https:\/\/doi.org\/10.1017\/S0004972722000399.","journal-title":"Bull. Aust. Math. Soc."},{"key":"1176_CR17","doi-asserted-by":"publisher","DOI":"10.1142\/3603","volume-title":"Quaternary Codes","author":"Z Wan","year":"1997","unstructured":"Wan Z.: Quaternary Codes. World Scientifc, Singapore (1997)."},{"issue":"1","key":"1176_CR18","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/S0019-9958(68)90779-1","volume":"13","author":"AD Wyner","year":"1968","unstructured":"Wyner A.D., Graham R.L.: An upper bound on minimum distance for a $$k$$-ary code. Inf. Control 13(1), 46\u201352 (1968).","journal-title":"Inf. Control"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-022-01176-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-022-01176-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-022-01176-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T20:07:11Z","timestamp":1682021231000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-022-01176-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,10]]},"references-count":18,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,5]]}},"alternative-id":["1176"],"URL":"https:\/\/doi.org\/10.1007\/s10623-022-01176-3","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,10]]},"assertion":[{"value":"30 July 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 September 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 December 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 January 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}