{"title":"Full weight spectrum one-orbit cyclic subspace codes","authors":"Chiara Castello, Olga Polverino, Ferdinando Zullo","doi":"10.1016/j.jcta.2024.106005","DOIUrl":null,"url":null,"abstract":"<div><div>For a linear Hamming metric code of length <em>n</em> over a finite field, the number of distinct weights of its codewords is at most <em>n</em>. The codes achieving the equality in the above bound were called full weight spectrum codes. In this paper, we will focus on the analogous class of codes within the framework of cyclic subspace codes. Cyclic subspace codes have garnered significant attention, particularly for their applications in random network coding to correct errors and erasures. We investigate one-orbit cyclic subspace codes that are <em>full weight spectrum</em> in this context. Utilizing number-theoretical results and combinatorial arguments, we provide a complete classification of full weight spectrum one-orbit cyclic subspace codes.</div></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"212 ","pages":"Article 106005"},"PeriodicalIF":0.9000,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series A","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0097316524001444","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
For a linear Hamming metric code of length n over a finite field, the number of distinct weights of its codewords is at most n. The codes achieving the equality in the above bound were called full weight spectrum codes. In this paper, we will focus on the analogous class of codes within the framework of cyclic subspace codes. Cyclic subspace codes have garnered significant attention, particularly for their applications in random network coding to correct errors and erasures. We investigate one-orbit cyclic subspace codes that are full weight spectrum in this context. Utilizing number-theoretical results and combinatorial arguments, we provide a complete classification of full weight spectrum one-orbit cyclic subspace codes.
期刊介绍:
The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.