{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:23:25Z","timestamp":1753885405315,"version":"3.41.2"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,1]]},"abstract":"<jats:p> In this paper, we will study the structure of [Formula: see text]-additive codes where [Formula: see text] is the well-known ring of 4 elements and [Formula: see text] is the ring given by [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text]. We will classify all maximum distance separable codes with respect to the Singleton bound (MDSS) over [Formula: see text] Then we will focus on [Formula: see text]-additive cyclic and constacyclic codes. We will find a unique set of generator polynomials for these codes and determine minimum spanning sets for them. We will also find the generator polynomials for the dual of any [Formula: see text]-additive cyclic or constacyclic code. <\/jats:p>","DOI":"10.1142\/s1793830922500665","type":"journal-article","created":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T07:25:12Z","timestamp":1648538712000},"source":"Crossref","is-referenced-by-count":0,"title":["\u21244R-additive cyclic and constacyclic codes and MDSS codes"],"prefix":"10.1142","volume":"15","author":[{"given":"Arazgol","family":"Ghajari","sequence":"first","affiliation":[{"name":"Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran"}]},{"given":"Kazem","family":"Khashyarmanesh","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran"}]},{"given":"Taher","family":"Abualrub","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE"}]},{"given":"Irfan","family":"Siap","sequence":"additional","affiliation":[{"name":"Jacodesmath Institute, Istanbul 34220, Turkey"}]}],"member":"219","published-online":{"date-parts":[[2022,3,28]]},"reference":[{"key":"S1793830922500665BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830917500100"},{"key":"S1793830922500665BIB002","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2014.2299791"},{"key":"S1793830922500665BIB003","doi-asserted-by":"publisher","DOI":"10.1504\/IJICOT.2015.072627"},{"key":"S1793830922500665BIB004","doi-asserted-by":"publisher","DOI":"10.1080\/00207160.2013.859854"},{"key":"S1793830922500665BIB005","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2632163"},{"key":"S1793830922500665BIB006","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.ffa.2017.03.001","volume":"48","author":"Aydogdu I.","year":"2017","journal-title":"Finite Fields Appl."},{"issue":"1","key":"S1793830922500665BIB007","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10623-010-9437-1","volume":"61","author":"Bilal M.","year":"2011","journal-title":"Des. 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