{"title":"Additive codes with few weights","authors":"Daniel Panario, Murat Sahin, Qiang Wang","doi":"10.1007/s12095-024-00720-3","DOIUrl":null,"url":null,"abstract":"<p>Additive codes have a wide range of applications. A classical nice and generic way to construct linear codes is via trace functions. In this paper, first, we generalize this method to construct additive codes. Then, we use this method to get some explicit additive codes. Computing Weil-like sums, we obtain parameters of these codes such as the length and weight distribution. We show that our codes have few weights.</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"44 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cryptography and Communications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12095-024-00720-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
Additive codes have a wide range of applications. A classical nice and generic way to construct linear codes is via trace functions. In this paper, first, we generalize this method to construct additive codes. Then, we use this method to get some explicit additive codes. Computing Weil-like sums, we obtain parameters of these codes such as the length and weight distribution. We show that our codes have few weights.
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