Designs, Codes and Cryptography最新文献_第4页

The weight hierarchy of decreasing norm-trace codes 递减规范跟踪代码的权重层次结构

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-01 DOI: 10.1007/s10623-025-01619-7

Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews, Rodrigo San-José

{"title":"The weight hierarchy of decreasing norm-trace codes","authors":"Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews, Rodrigo San-José","doi":"10.1007/s10623-025-01619-7","DOIUrl":"https://doi.org/10.1007/s10623-025-01619-7","url":null,"abstract":"The Generalized Hamming weights and their relative version, which generalize the minimum distance of a linear code, are relevant to numerous applications, including coding on the wire-tap channel of type II, t-resilient functions, bounding the cardinality of the output in list decoding algorithms, ramp secret sharing schemes, and quantum error correction. The generalized Hamming weights have been determined for some families of codes, including Cartesian codes and Hermitian one-point codes. In this paper, we determine the generalized Hamming weights of decreasing norm-trace codes, which are linear codes defined by evaluating sets of monomials that are closed under divisibility on the rational points of the extended norm-trace curve given by (x^{u} = y^{q^{s - 1}} + y^{q^{s - 2}} + cdots + y) over the finite field of cardinality (q^s), where u is a positive divisor of (frac{q^s - 1}{q - 1}). As a particular case, we obtain the weight hierarchy of one-point norm-trace codes and recover the result of Barbero and Munuera (2001) giving the weight hierarchy of one-point Hermitian codes. We also study the relative generalized Hamming weights for these codes and use them to construct impure quantum codes with excellent parameters.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"22 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143745305","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}

引用次数: 0

On the cycle structure of a class of Galois NFSRs: component sequences possessing identical periods 一类伽罗瓦NFSRs的循环结构：具有相同周期的分量序列

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-29 DOI: 10.1007/s10623-025-01616-w

Xiao-juan Wang, Tian Tian, Wen-feng Qi

引用次数: 0

Universal partial tori 泛偏环面

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-27 DOI: 10.1007/s10623-025-01609-9

William D. Carey, Matthew David Kearney, Rachel Kirsch, Stefan Popescu

引用次数: 0

Studying the isomorphism of NFSRs via a general framework of bijections 用双射的一般框架研究nfsr的同构性

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-27 DOI: 10.1007/s10623-025-01622-y

Jingtao Xiong, Jianghua Zhong, Dongdai Lin

{"title":"Studying the isomorphism of NFSRs via a general framework of bijections","authors":"Jingtao Xiong, Jianghua Zhong, Dongdai Lin","doi":"10.1007/s10623-025-01622-y","DOIUrl":"https://doi.org/10.1007/s10623-025-01622-y","url":null,"abstract":"Nonlinear feedback shift registers (NFSRs) are used in many recent stream ciphers as their main building blocks. Two NFSRs are said to be isomorphic if their state diagrams are isomorphic, and to be equivalent if their sets of output sequences are equal. So far, numerous work has been done on the equivalence of NFSRs with same bit number, but much less has been done on their isomorphism. Actually, the equivalence problem of NFSRs with same bit number can be transformed to their isomorphism problem. The latter can be solved if the bijection between their states and its inverse can be explicitly expressed, which are quite hard to get in general. This paper studies the isomorphism of NFSRs by building a general framework for bijections. It first gives basic bijections. It then presents a unified formula for bijections, and discloses that any bijection can be expressed as a composite of finite basic bijections, setting up a general framework for bijections. Based on the general framework, the paper discloses in theory how to obtain all Galois NFSRs that are isomorphic to a given NFSR, and then reveals the bijections between the states of the previous types of Galois NFSRs and their own equivalent Fibonacci NFSRs. Finally, it proposes a new type of Galois NFSRs that are isomorphic and further equivalent to Fibonacci NFSRs, covering and improving most previous types of Galois NFSRs known to be equivalent to Fibonacci NFSRs.\u0000","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"183 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143713069","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}

引用次数: 0

The complete weight enumerator of the square of one-weight irreducible cyclic codes 一权不可约循环码平方的完全权枚举数

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-22 DOI: 10.1007/s10623-025-01620-0

Canze Zhu

引用次数: 0

Limitations of the decoding-to-LPN reduction via code smoothing 通过代码平滑降低解码到lpn的局限性

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-22 DOI: 10.1007/s10623-025-01617-9

Madhura Pathegama, Alexander Barg

引用次数: 0

Binary stretch embedding of weighted graphs 加权图的二元拉伸嵌入

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-21 DOI: 10.1007/s10623-025-01608-w

Javad Ebrahimi Boroojeni, Mehri Oghbaei Bonab

{"title":"Binary stretch embedding of weighted graphs","authors":"Javad Ebrahimi Boroojeni, Mehri Oghbaei Bonab","doi":"10.1007/s10623-025-01608-w","DOIUrl":"https://doi.org/10.1007/s10623-025-01608-w","url":null,"abstract":"In this paper, we introduce and study the problem of binary stretch embedding of edge-weighted graphs in both integer and fractional settings. Roughly speaking, the binary stretch embedding problem for a weighted graph G is to find a mapping from the vertex set of G, to the vertices of a hypercube graph such that the distance between every pair of the vertices is not reduced under the mapping, hence the name binary stretch embedding. The minimum dimension of a hypercube for which such a stretch embedding exists is called the binary addressing number of G. We show that the binary addressing number of weighted graphs is the optimum value of an integer program. The optimum value for the corresponding linear relaxation problem is called the fractional binary addressing number of G. This embedding type problem is closely related to the well-known addressing problem of Graham and Pollak and isometric hypercube embedding problem of Firsov. Using tools and techniques such as Hadamard codes and the linear programming theory help us to find upper and lower bounds, approximations, or exact values of the binary addressing number and the fractional variant of graphs. As an application of our results, we derive improved upper bounds or exact values of the maximum size of Lee metric codes of certain parameters.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"41 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143666542","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}

引用次数: 0

Additive combinatorial designs 加性组合设计

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-20 DOI: 10.1007/s10623-025-01594-z

Marco Buratti, Francesca Merola, Anamari Nakić

{"title":"Additive combinatorial designs","authors":"Marco Buratti, Francesca Merola, Anamari Nakić","doi":"10.1007/s10623-025-01594-z","DOIUrl":"https://doi.org/10.1007/s10623-025-01594-z","url":null,"abstract":"A (2-(v, k, lambda )) design is additive if, up to isomorphism, the point set is a subset of an abelian group G and every block is zero-sum. This definition was introduced in Caggegi et al. (J Algebr Comb 45:271-294, 2017) and was the starting point of an interesting new theory. Although many additive designs have been constructed and known designs have been shown to be additive, these structures seem quite hard to construct in general, particularly when we look for additive Steiner 2-designs. One might generalize additive Steiner 2-designs in a natural way to graph decompositions as follows: given a simple graph (Gamma ), an additive ((K_v,Gamma ))-design is a decomposition of the graph (K_v) into subgraphs (blocks) (B_1,dots ,B_t) all isomorphic to (Gamma ), such that the vertex set (V(K_v)) is a subset of an abelian group G, and the sets (V(B_1), dots , V(B_t)) are zero-sum in G. In this work we begin the study of additive ((K_v,Gamma ))-designs: we develop different tools instrumental in constructing these structures, and apply them to obtain some infinite classes of designs and many sporadic examples. We will consider decompositions into various graphs (Gamma ), for instance cycles, paths, and k-matchings. Similar ideas will also allow us to present here a sporadic additive 2-(124, 4, 1) design.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"34 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143661406","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}

引用次数: 0

An attack on p-adic lattice public-key encryption cryptosystems and signature schemes 对 p 演算网格公钥加密密码系统和签名方案的攻击

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-18 DOI: 10.1007/s10623-025-01618-8

Chi Zhang

引用次数: 0

A new framework for fast homomorphic matrix multiplication 一个新的快速同态矩阵乘法框架

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-15 DOI: 10.1007/s10623-025-01614-y

Xiaopeng Zheng, Hongbo Li, Dingkang Wang

引用次数: 0