Designs, Codes and Cryptography最新文献

{"title":"Incidence of lines, points and planes in PG(3, q) with respect to the twisted cubic","authors":"Krishna Kaipa, Puspendu Pradhan","doi":"10.1007/s10623-026-01920-z","DOIUrl":"https://doi.org/10.1007/s10623-026-01920-z","url":null,"abstract":"We consider the orbits of the group <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mi>G</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>q</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$G=PGL_2(q)$$end{document}</tex-math></alternatives></inline-formula> on the points, lines and planes of the projective space <italic>PG</italic>(3, <italic>q</italic>) over a finite field <inline-formula><alternatives><mml:math><mml:msub><mml:mi mathvariant=\"double-struck\">F</mml:mi><mml:mi>q</mml:mi></mml:msub></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathbb {F}_q$$end{document}</tex-math></alternatives></inline-formula> of characteristic different from 2 and 3. The points of <italic>PG</italic>(3, <italic>q</italic>) can be identified with projective space of binary cubic forms, and the set <inline-formula><alternatives><mml:math><mml:mi mathvariant=\"script\">L</mml:mi></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathcal {L}$$end{document}</tex-math></alternatives></inline-formula> of lines of <italic>PG</italic>(3, <italic>q</italic>) can be thought of as pencils of cubic forms. The action of <italic>G</italic> on <italic>PG</italic>(1, <italic>q</italic>) naturally induces an action of <italic>G</italic> on binary cubic forms <italic>f</italic>(<italic>X</italic>, <italic>Y</italic>). The points of <italic>PG</italic>(3, <italic>q</italic>) decompose into five <italic>G</italic> orbits. The <italic>G</italic> orbits on <inline-formula><alternatives><mml:math><mml:mi mathvariant=\"script\">L</mml:mi></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathcal {L}$$end{document}</tex-math></alternatives></inline-formula> were recently obtained by the authors. Let <inline-formula><alternatives><mml:math><mml:mi mathvariant=\"script\">I</mml:mi></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathcal {I}$$end{document}</tex-math></","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"17 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148687825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Divisible design graphs obtained by plugging a difference set into a construction for antipodal distance-regular graphs of diameter 3","authors":"Bart De Bruyn, Sergey Goryainov, Ruilin Ma, Ruihan Xie","doi":"10.1007/s10623-026-01922-x","DOIUrl":"https://doi.org/10.1007/s10623-026-01922-x","url":null,"abstract":"In this paper, we present a new construction of divisible design graphs with new parameters, obtained by plugging a difference set of a quotient group into a known construction of antipodal distance-regular graphs of diameter 3. Also, we show that in characteristic 2 the new divisible design graphs are Cayley graphs over an elementary abelian 2-group.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"37 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148687907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Locally Recoverable Codes with availability from a family of fibered surfaces","authors":"Cecília Salgado, Lara Vicino","doi":"10.1007/s10623-026-01904-z","DOIUrl":"https://doi.org/10.1007/s10623-026-01904-z","url":null,"abstract":"We construct Locally Recoverable Codes (LRCs) with availability 2 from a family of fibered surfaces. To obtain the locality and availability properties, and to estimate the minimum distance of the codes, we combine techniques coming from the theory of one-variable function fields and from the theory of fibrations on surfaces. When the locality parameter is <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$r=3$$end{document}</tex-math></alternatives></inline-formula>, we obtain a sharp bound on the minimum distance of the codes. In that case, we give a geometric interpretation of our codes in terms of doubly elliptic surfaces. In particular, this provides the first instance of an error correcting code constructed using a (doubly elliptic) K3 surface.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"26 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148687824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linearized Polynomial Chinese Remainder codes","authors":"Philippe Gaborit, Camille Garnier, Olivier Ruatta","doi":"10.1007/s10623-026-01911-0","DOIUrl":"https://doi.org/10.1007/s10623-026-01911-0","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148587083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterization of $$ell $$-form plateaued functions via association schemes","authors":"Jiaxin Wang, Jong Yoon Hyun, Yoonjin Lee, Yansheng Wu","doi":"10.1007/s10623-026-01914-x","DOIUrl":"https://doi.org/10.1007/s10623-026-01914-x","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"8 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148587084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Balanced $$(mathbb {Z}_{m}times mathbb {Z}_{n},{4,5},1)$$-difference packings and their related OOSPCs","authors":"Rong Pan, Lidong Wang, Xiaomiao Wang","doi":"10.1007/s10623-026-01910-1","DOIUrl":"https://doi.org/10.1007/s10623-026-01910-1","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"13 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148586781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the second generalized covering radius for binary primitive triple-error-correcting BCH codes","authors":"Ferruh Özbudak, İlknur Öztürk","doi":"10.1007/s10623-026-01903-0","DOIUrl":"https://doi.org/10.1007/s10623-026-01903-0","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"60 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148538146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of Hermitian hulls of Reed–Solomon codes and EAQECCs","authors":"Hailong Xu, Qi Liu, Haiyan Zhou","doi":"10.1007/s10623-026-01907-w","DOIUrl":"https://doi.org/10.1007/s10623-026-01907-w","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"17 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148538150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Construction of balanced $$2^{k}$$-variable rotation symmetric Boolean functions with optimal algebraic immunity","authors":"Jiao Du, Xiaoting Chen, Hui Zhang, Longjiang Qu, Chao Li","doi":"10.1007/s10623-026-01906-x","DOIUrl":"https://doi.org/10.1007/s10623-026-01906-x","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"76 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148538147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Block-transitive designs with a poset of imprimitive partitions","authors":"Carmen Amarra, Alice Devillers, Cheryl E. Praeger","doi":"10.1007/s10623-026-01891-1","DOIUrl":"https://doi.org/10.1007/s10623-026-01891-1","url":null,"abstract":"We study block designs which admit an automorphism group that is transitive on blocks and points, and leaves invariant every partition in a given finite poset of partitions of the point set. The full stabiliser <jats:italic>G</jats:italic> of all the partitions in the poset is a generalised wreath product. We use the theory of generalised wreath products to give necessary and sufficient conditions, in terms of the ‘array’ of a point-subset <jats:italic>B</jats:italic> , for the set of <jats:italic>G</jats:italic> -images of <jats:italic>B</jats:italic> to form the block-set of a <jats:italic>G</jats:italic> -block-transitive 2-design. This generalises previous results for the special cases where the poset is a chain or an anti-chain. We also give explicit infinite families of examples of 2-designs for each poset involving three proper partitions, and for the famous <jats:italic>N</jats:italic> -poset with four partitions. (Posets with two proper partitions have been treated previously.) This suggests the problem of finding explicit examples for other posets.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"246 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148538148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}