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Block codes on pomset metric 在pomset度量上的块代码
Asian-European Journal of Mathematics Pub Date : 2023-06-29 DOI: 10.1142/s1793557123501711
Atul Kumar Shriwastva, R. S. Selvaraj
{"title":"Block codes on pomset metric","authors":"Atul Kumar Shriwastva, R. S. Selvaraj","doi":"10.1142/s1793557123501711","DOIUrl":"https://doi.org/10.1142/s1793557123501711","url":null,"abstract":"Given a regular multiset [Formula: see text] on [Formula: see text], a partial order [Formula: see text] on [Formula: see text], and a label map [Formula: see text] defined by [Formula: see text] with [Formula: see text], we define a pomset block metric [Formula: see text] on the direct sum [Formula: see text] of [Formula: see text] based on the pomset [Formula: see text]. The pomset block metric extends the classical pomset metric introduced by Sudha and Selvaraj and generalizes the poset block metric introduced by Alves et al. over [Formula: see text]. The space [Formula: see text] is called the pomset block space and we determine the complete weight distribution of it. Further, [Formula: see text]-perfect pomset block codes for ideals with partial and full counts are described. Then, for block codes with chain pomset, the packing radius and Singleton bound are established. The relation between maximum distance separable (MDS) codes and [Formula: see text]-perfect codes for any ideal [Formula: see text] is investigated. Moreover, the duality theorem for an MDS pomset block code is established when all the blocks have the same size.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134998997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inequalities for the polar derivative of a polynomial with restricted zeros 具有限制零的多项式的极导数的不等式
Asian-European Journal of Mathematics Pub Date : 2023-06-21 DOI: 10.1142/s179355712350167x
W. M. Shah, Raihana Rashid
{"title":"Inequalities for the polar derivative of a polynomial with restricted zeros","authors":"W. M. Shah, Raihana Rashid","doi":"10.1142/s179355712350167x","DOIUrl":"https://doi.org/10.1142/s179355712350167x","url":null,"abstract":"Let [Formula: see text] be a polynomial of degree at most [Formula: see text] with real or complex coefficients, then by a prize winning result of Bernstein [Formula: see text] In this paper, we assume that [Formula: see text] has a zero of multiplicity [Formula: see text] at a point inside the unit disc and the remaining zeros outside or inside the disc of radius [Formula: see text] and prove some Bernstein-type inequalities. We also draw the attention of readers to the wrong conclusion of a result due to [Mir and Wani, A note on two recent results about polynomials with restricted zeros, J. Math. Inequalities, 14 (2020) 45–50].","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136355307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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