{"title":"Several classes of wide minimal binary linear codes based on general Maiorana-McFarland class","authors":"Xiaoni Du , Siqi Gao , Wenping Yuan , Xingbin Qiao","doi":"10.1016/j.disc.2025.114642","DOIUrl":null,"url":null,"abstract":"<div><div>Minimal linear codes have important applications in secret sharing schemes and secure two-party computation. In this paper, we extend the construction of wide minimal binary linear codes presented by Ding et al. <span><span>[8]</span></span> (2018) to a more general case. More specifically, we first construct a class of Boolean functions belonging to the general Maiorana-McFarland class with more flexible parameters. Then we provide a framework for examining the Walsh transform of the new functions via the Krawtchouk polynomial. Finally, we obtain several classes of wide minimal binary linear codes with a few weights and determine their weight distribution explicitly. Our results cover all the related existing ones.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 12","pages":"Article 114642"},"PeriodicalIF":0.7000,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X2500250X","RegionNum":3,"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
Minimal linear codes have important applications in secret sharing schemes and secure two-party computation. In this paper, we extend the construction of wide minimal binary linear codes presented by Ding et al. [8] (2018) to a more general case. More specifically, we first construct a class of Boolean functions belonging to the general Maiorana-McFarland class with more flexible parameters. Then we provide a framework for examining the Walsh transform of the new functions via the Krawtchouk polynomial. Finally, we obtain several classes of wide minimal binary linear codes with a few weights and determine their weight distribution explicitly. Our results cover all the related existing ones.
期刊介绍:
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.