Designs, Codes and Cryptography最新文献_第2页

The geometry of covering codes in the sum–rank metric 和秩度量中覆盖码的几何形状

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-09 DOI: 10.1007/s10623-025-01628-6

Matteo Bonini, Martino Borello, Eimear Byrne

引用次数: 0

Fast multiplication and the PLWE–RLWE equivalence for an infinite family of maximal real subfields of cyclotomic fields 分环场无穷一族极大实子域的快速乘法和PLWE-RLWE等价

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-07 DOI: 10.1007/s10623-025-01601-3

Joonas Ahola, Iván Blanco-Chacón, Wilmar Bolaños, Antti Haavikko, Camilla Hollanti, Rodrigo M. Sánchez-Ledesma

{"title":"Fast multiplication and the PLWE–RLWE equivalence for an infinite family of maximal real subfields of cyclotomic fields","authors":"Joonas Ahola, Iván Blanco-Chacón, Wilmar Bolaños, Antti Haavikko, Camilla Hollanti, Rodrigo M. Sánchez-Ledesma","doi":"10.1007/s10623-025-01601-3","DOIUrl":"https://doi.org/10.1007/s10623-025-01601-3","url":null,"abstract":"We prove the equivalence between the Ring Learning With Errors (RLWE) and the Polynomial Learning With Errors (PLWE) problems for the maximal totally real subfield of the (2^r 3^s)th cyclotomic field for (r ge 3) and (s ge 1). Moreover, we describe a fast algorithm for computing the product of two elements in the ring of integers of these subfields. This multiplication algorithm has quasilinear complexity in the dimension of the field, as it makes use of the fast Discrete Cosine Transform (DCT). Our approach assumes that the two input polynomials are given in a basis of Chebyshev-like polynomials, in contrast to the customary power basis. To validate this assumption, we prove that the change of basis from the power basis to the Chebyshev-like basis can be computed with ({mathcal {O}}(n log n)) arithmetic operations, where n is the problem dimension. Finally, we provide a heuristic and theoretical comparison of the vulnerability to some attacks for the pth cyclotomic field versus the maximal totally real subextension of the 4pth cyclotomic field for a reasonable set of parameters of cryptographic size.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"74 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143797694","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

Constructions of binary cyclic codes with minimum weights exceeding the square-root lower bound 最小权值超过平方根下界的二进制循环码的构造

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-07 DOI: 10.1007/s10623-025-01621-z

Hai Liu, Chunyu Gan, Chengju Li, Xueying Shi

{"title":"Constructions of binary cyclic codes with minimum weights exceeding the square-root lower bound","authors":"Hai Liu, Chunyu Gan, Chengju Li, Xueying Shi","doi":"10.1007/s10623-025-01621-z","DOIUrl":"https://doi.org/10.1007/s10623-025-01621-z","url":null,"abstract":"Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Constructing binary cyclic codes with parameters ([n, frac{n+1}{2}, d ge sqrt{n}]) is an interesting topic in coding theory, as their minimum distances have a square-root bound. Let (n=2^lambda -1), where (lambda ) has three forms: (p^2, p_1p_2, 2p_2) for odd primes (p, p_1, p_2). In this paper, we mainly construct several classes of binary cyclic codes with parameters ([2^lambda -1, k ge 2^{lambda -1}, d ge sqrt{n}]). Specifically, the binary cyclic codes ({mathcal {C}}_{(1, p^2)}), ({mathcal {C}}_{(1, 2p_2)}), ({mathcal {C}}_{(2, 2p_2)}), and ({mathcal {C}}_{(1, p_1p_2)}) have minimum distance (d ge sqrt{n}) though their dimensions satisfy (k > frac{n+1}{2}). Moreover, two classes of binary cyclic codes ({mathcal {C}}_{(2, p^2)}) and ({mathcal {C}}_{(2, p_1p_2)}) with dimension (k= frac{n+1}{2}) and minimum distance d much exceeding the square-root bound are presented, which extends the results given by Sun, Li, and Ding [30]. In fact, the rate of these two classes of binary cyclic codes are around (frac{1}{2}) and the lower bounds on their minimum distances are close to (frac{n}{log _2 n}). In addition, their extended codes are also investigated.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"21 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143797794","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

Quantum codes and irreducible products of characters 量子码与字符的不可约积

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-05 DOI: 10.1007/s10623-025-01599-8

Eric Kubischta, Ian Teixeira

引用次数: 0

Constructions of locally recoverable codes with large availability 具有大可用性的局部可恢复代码的构造

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-05 DOI: 10.1007/s10623-025-01624-w

Giacomo Micheli, Vincenzo Pallozzi Lavorante, Abhi Shukul, Noah Smith

引用次数: 0

A new method for erasure decoding of convolutional codes 一种新的卷积码擦除译码方法

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-03 DOI: 10.1007/s10623-025-01623-x

Julia Lieb, Raquel Pinto, Carlos Vela

引用次数: 0

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