Designs, Codes and Cryptography最新文献_第9页

Optimal $$(r,delta )$$ -LRCs from monomial-Cartesian codes and their subfield-subcodes 来自单项式-笛卡尔码及其子域-子码的最优 $$(r,delta )$$ -LRCs

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-05-02 DOI: 10.1007/s10623-024-01403-z

C. Galindo, F. Hernando, H. Martín-Cruz

引用次数: 0

Computing gluing and splitting $$(ell ,ell )$$ -isogenies 计算粘合与分裂 $$(ell ,ell )$$ - 等因关系

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-05-02 DOI: 10.1007/s10623-024-01413-x

Song Tian

引用次数: 0

Characterization of weakly regular p-ary bent functions of $$ell $$ -form $$ell $$ -form 的弱正则 p-ary 弯曲函数的特征

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-05-02 DOI: 10.1007/s10623-024-01411-z

Jong Yoon Hyun, Jungyun Lee, Yoonjin Lee

{"title":"Characterization of weakly regular p-ary bent functions of $$ell $$ -form","authors":"Jong Yoon Hyun, Jungyun Lee, Yoonjin Lee","doi":"10.1007/s10623-024-01411-z","DOIUrl":"https://doi.org/10.1007/s10623-024-01411-z","url":null,"abstract":"We study the essential properties of weakly regular p-ary bent functions of (ell )-form, where a p-ary function is from (mathbb {F}_{p^m}) to (mathbb {F}_p). We observe that most of studies on a weakly regular p-ary bent function f with (f(0)=0) of (ell )-form always assume the gcd-condition: (gcd (ell -1,p-1)=1). We first show that whenever considering weakly regular p-ary bent functions f with (f(0) = 0) of (ell )-form, we can drop the gcd-condition; using the gcd-condition, we also obtain a characterization of a weakly regular bent function of (ell )-form. Furthermore, we find an additional characterization for weakly regular bent functions of (ell )-form; we consider two cases m being even or odd. Let f be a weakly regular bent function of (ell )-form preserving the zero element; then in the case that m is odd, we show that f satisfies (gcd (ell ,p-1)=2). On the other hand, when m is even and f is also non-regular, we show that f satisfies (gcd (ell ,p-1)=2) as well. In addition, we present two explicit families of regular bent functions of (ell )-form in terms of the gcd-condition.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140890399","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 packing density of Lee spheres 关于李球的堆积密度

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-04-30 DOI: 10.1007/s10623-024-01410-0

Ang Xiao, Yue Zhou

引用次数: 0

Subgroup total perfect codes in Cayley sum graphs Cayley 和图中的子群完全码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-04-29 DOI: 10.1007/s10623-024-01405-x

Xiaomeng Wang, Lina Wei, Shou-Jun Xu, Sanming Zhou

{"title":"Subgroup total perfect codes in Cayley sum graphs","authors":"Xiaomeng Wang, Lina Wei, Shou-Jun Xu, Sanming Zhou","doi":"10.1007/s10623-024-01405-x","DOIUrl":"https://doi.org/10.1007/s10623-024-01405-x","url":null,"abstract":"Let (Gamma ) be a graph with vertex set V, and let a, b be nonnegative integers. An (a, b)-regular set in (Gamma ) is a nonempty proper subset D of V such that every vertex in D has exactly a neighbours in D and every vertex in (V setminus D) has exactly b neighbours in D. In particular, a (1, 1)-regular set is called a total perfect code. Let G be a finite group and S a square-free subset of G closed under conjugation. The Cayley sum graph (textrm{CayS}(G,S)) of G is the graph with vertex set G such that two vertices x, y are adjacent if and only if (xy in S). A subset (respectively, subgroup) D of G is called an (a, b)-regular set (respectively, subgroup (a, b)-regular set) of G if there exists a Cayley sum graph of G which admits D as an (a, b)-regular set. We obtain two necessary and sufficient conditions for a subgroup of a finite group G to be a total perfect code in a Cayley sum graph of G. We also obtain two necessary and sufficient conditions for a subgroup of a finite abelian group G to be a total perfect code of G. We classify finite abelian groups whose all non-trivial subgroups of even order are total perfect codes of the group, and as a corollary we obtain that a finite abelian group has the property that every non-trivial subgroup is a total perfect code if and only if it is isomorphic to an elementary abelian 2-group. We prove that, for a subgroup H of a finite abelian group G and any pair of positive integers (a, b) within certain ranges depending on H, H is an (a, b)-regular set of G if and only if it is a total perfect code of G. Finally, we give a classification of subgroup total perfect codes of a cyclic group, a dihedral group and a generalized quaternion group.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140817584","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

Special directions on the finite affine plane 有限仿射平面上的特殊方向

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-04-29 DOI: 10.1007/s10623-024-01404-y

Gergely Kiss, Gábor Somlai

引用次数: 0

Small weight codewords of projective geometric codes II 投影几何码的小权重码元 II

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-04-28 DOI: 10.1007/s10623-024-01397-8

Sam Adriaensen, Lins Denaux

引用次数: 0

Further results on covering codes with radius R and codimension $$tR+1$$ 半径为 R、标度为 $$tR+1$$ 的覆盖编码的进一步结果

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-04-27 DOI: 10.1007/s10623-024-01402-0

Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco

{"title":"Further results on covering codes with radius R and codimension $$tR+1$$","authors":"Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco","doi":"10.1007/s10623-024-01402-0","DOIUrl":"https://doi.org/10.1007/s10623-024-01402-0","url":null,"abstract":"The length function (ell _q(r,R)) is the smallest possible length n of a q-ary linear ([n,n-r]_qR) code with codimension (redundancy) r and covering radius R. Let (s_q(N,rho )) be the smallest size of a (rho )-saturating set in the projective space (textrm{PG}(N,q)). There is a one-to-one correspondence between ([n,n-r]_qR) codes and ((R-1))-saturating n-sets in (textrm{PG}(r-1,q)) that implies (ell _q(r,R)=s_q(r-1,R-1)). In this work, for (Rge 3), new asymptotic upper bounds on (ell _q(tR+1,R)) are obtained in the following form: $$begin{aligned}&bullet ~ell _q(tR+1,R) =s_q(tR,R-1)&hspace{0.4cm} le root R of {frac{R!}{R^{R-2}}}cdot q^{(r-R)/R}cdot root R of {ln q}+o(q^{(r-R)/R}), hspace{0.3cm} r=tR+1,~tge 1,&hspace{0.4cm}~ qtext { is an arbitrary prime power},~qtext { is large enough};&bullet ~text { if additionally }Rtext { is large enough, then }root R of {frac{R!}{R^{R-2}}}thicksim frac{1}{e}thickapprox 0.3679. end{aligned}$$The new bounds are essentially better than the known ones. For (t=1), a new construction of ((R-1))-saturating sets in the projective space (textrm{PG}(R,q)), providing sets of small sizes, is proposed. The ([n,n-(R+1)]_qR) codes, obtained by the construction, have minimum distance (R + 1), i.e. they are almost MDS (AMDS) codes. These codes are taken as the starting ones in the lift-constructions (so-called “(q^m)-concatenating constructions”) for covering codes to obtain infinite families of codes with growing codimension (r=tR+1), (tge 1).","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140651611","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

Using $$P_tau $$ property for designing bent functions provably outside the completed Maiorana–McFarland class 利用 $$P_tau$ 属性设计弯曲函数，可证明其在已完成的马约拉纳-麦克法兰类之外

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-04-22 DOI: 10.1007/s10623-024-01407-9

Enes Pasalic, Amar Bapić, Fengrong Zhang, Yongzhuang Wei

{"title":"Using $$P_tau $$ property for designing bent functions provably outside the completed Maiorana–McFarland class","authors":"Enes Pasalic, Amar Bapić, Fengrong Zhang, Yongzhuang Wei","doi":"10.1007/s10623-024-01407-9","DOIUrl":"https://doi.org/10.1007/s10623-024-01407-9","url":null,"abstract":"In this article, we identify certain instances of bent functions, constructed using the so-called (P_tau ) property, that are provably outside the completed Maiorana–McFarland (({mathcal{M}mathcal{M}}^#)) class. This also partially answers an open problem in posed by Kan et al. (IEEE Trans Inf Theory, https://doi.org/10.1109/TIT.2022.3140180, 2022). We show that this design framework (using the (P_tau ) property), can provide instances of bent functions that are outside the known classes of bent functions, including the classes ({mathcal{M}mathcal{M}}^#), ({{mathcal {C}}},{{mathcal {D}}}) and ({{mathcal {D}}}_0), where the latter three were introduced by Carlet in the early nineties. We provide two generic methods for identifying such instances, where most notably one of these methods uses permutations that may admit linear structures. For the first time, a set of sufficient conditions for the functions of the form (h(y,z)=Tr(ypi (z)) + G_1(Tr_1^m(alpha _1y),ldots ,Tr_1^m(alpha _ky))G_2(Tr_1^m(beta _{k+1}z),ldots ,Tr_1^m(beta _{tau }z))+ G_3(Tr_1^m(alpha _1y),ldots ,Tr_1^m(alpha _ky))) to be bent and outside ({mathcal{M}mathcal{M}}^#) is specified without a strong assumption that the components of the permutation (pi ) do not admit linear structures.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140636276","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

Chain-imprimitive, flag-transitive 2-designs 链式祈使句、旗式祈使句 2 种设计

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-04-20 DOI: 10.1007/s10623-024-01400-2

Carmen Amarra, Alice Devillers, Cheryl E. Praeger

引用次数: 0