{"title":"Completely regular codes in graphs covered by a Hamming graph","authors":"Sergey Goryainov,Denis Krotov","doi":"10.1007/s10623-026-01955-2","DOIUrl":"https://doi.org/10.1007/s10623-026-01955-2","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"68 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208919","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":"A multiset approach to MacWilliams identities","authors":"Hopein Christofen Tang","doi":"10.1007/s10623-026-01951-6","DOIUrl":"https://doi.org/10.1007/s10623-026-01951-6","url":null,"abstract":"Abstract We interpret the symmetrized weight enumerator of linear codes over finite commutative Frobenius rings as a summation over multisets and thereby provide a new proof of the MacWilliams identity for the symmetrized weight enumerator. The proof and the identity are expressed in combinatorial terms that do not require generating characters. We also generalize the symmetrized weight enumerator with respect to supports and codeword tuples, and our multiset approach enables us to derive new and general MacWilliams identities expressed in combinatorial terms.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"16 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208918","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":"Maximal sets of mutually orthogonal frequency squares and Doehlert-Klee designs","authors":"Carly Bodkin,Nicholas J. Cavenagh,Ian M. Wanless","doi":"10.1007/s10623-026-01944-5","DOIUrl":"https://doi.org/10.1007/s10623-026-01944-5","url":null,"abstract":"Abstract A binary frequency square of type $$(n;lambda _0,lambda _1)$$ ( n ; λ 0 , λ 1 ) is a (0, 1)-matrix of order n with $$lambda _0$$ λ 0 zeros and $$lambda _1$$ λ 1 ones in each row and in each column. Two such squares are orthogonal if there are exactly $$lambda _1^2$$ λ 1 2 cells where both squares contain ones. A set of binary MOFS is a set of binary frequency squares in which each pair is orthogonal. A set of binary MOFS of type $$(n;lambda _0,lambda _1)$$ ( n ; λ 0 , λ 1 ) is type maximal if there is no square of the type $$(n;lambda _0,lambda _1)$$ ( n ; λ 0 , λ 1 ) that is orthogonal to every square in the set. A Doehlert-Klee design consists of points $$mathcal {V}$$ V and blocks $$mathcal {B}$$ B , where every pair of points occurs in precisely $$Lambda $$ Λ blocks and every point occurs in precisely R blocks, where $$R^2=Lambda |mathcal {B}|$$ R 2 = Λ | B | . We show that sets of binary MOFS are equivalent to a particular kind of Doehlert-Klee design. In a distinct application, Doehlert-Klee designs can also be used to construct sets of binary MOFS that are cyclically generated from their first rows. We use these connections to find new constructions for sets of type-maximal binary MOFS.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"60 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149049474","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":"A class of locally differentially 4-uniform power functions with Niho exponents","authors":"Haode Yan,Kangquan Li","doi":"10.1007/s10623-026-01950-7","DOIUrl":"https://doi.org/10.1007/s10623-026-01950-7","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"93 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149049445","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 minimum length of binary linear codes","authors":"Tatsuya Maruta,Taiki Tochiyama,Keita Yasufuku","doi":"10.1007/s10623-026-01947-2","DOIUrl":"https://doi.org/10.1007/s10623-026-01947-2","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"107 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149049443","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":"Infinite families of $$textrm{t}$$-error-correcting binary cyclic codes from sparse polynomials over $$mathbb {F}_{2^n}$$","authors":"Yan-Ping Wang,Dengguo Feng","doi":"10.1007/s10623-026-01949-0","DOIUrl":"https://doi.org/10.1007/s10623-026-01949-0","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"15 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149049446","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":"Embedding linear codes over $${mathbb {Z}}_4$$ into self-orthogonal codes","authors":"Junmin An,Jon-Lark Kim,San Ling","doi":"10.1007/s10623-026-01948-1","DOIUrl":"https://doi.org/10.1007/s10623-026-01948-1","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"107 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149049475","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":"Unbounded quadratic functional encryption and more from pairings","authors":"Junichi Tomida","doi":"10.1007/s10623-026-01928-5","DOIUrl":"https://doi.org/10.1007/s10623-026-01928-5","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"13 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149049444","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 combinatorial complexity of bounded sparse Learning With Errors (sLWE)","authors":"Abul Kalam,Santanu Sarkar,Willi Meier","doi":"10.1007/s10623-026-01938-3","DOIUrl":"https://doi.org/10.1007/s10623-026-01938-3","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"166 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149049473","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}