Advances in Mathematics of Communications最新文献_第6页

New quantum codes from skew constacyclic codes 从偏常环码出发的新量子码

IF 0.9 4区计算机科学

Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2021028

Ram Krishna Verma, O. Prakash, A. Singh, H. Islam

{"title":"New quantum codes from skew constacyclic codes","authors":"Ram Krishna Verma, O. Prakash, A. Singh, H. Islam","doi":"10.3934/amc.2021028","DOIUrl":"https://doi.org/10.3934/amc.2021028","url":null,"abstract":"For an odd prime <inline-formula><tex-math id=\"M1\">begin{document}$ p $end{document}</tex-math></inline-formula> and positive integers <inline-formula><tex-math id=\"M2\">begin{document}$ m $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M3\">begin{document}$ ell $end{document}</tex-math></inline-formula>, let <inline-formula><tex-math id=\"M4\">begin{document}$ mathbb{F}_{p^m} $end{document}</tex-math></inline-formula> be the finite field with <inline-formula><tex-math id=\"M5\">begin{document}$ p^{m} $end{document}</tex-math></inline-formula> elements and <inline-formula><tex-math id=\"M6\">begin{document}$ R_{ell,m} = mathbb{F}_{p^m}[v_1,v_2,dots,v_{ell}]/langle v^{2}_{i}-1, v_{i}v_{j}-v_{j}v_{i}rangle_{1leq i, jleq ell} $end{document}</tex-math></inline-formula>. Thus <inline-formula><tex-math id=\"M7\">begin{document}$ R_{ell,m} $end{document}</tex-math></inline-formula> is a finite commutative non-chain ring of order <inline-formula><tex-math id=\"M8\">begin{document}$ p^{2^{ell} m} $end{document}</tex-math></inline-formula> with characteristic <inline-formula><tex-math id=\"M9\">begin{document}$ p $end{document}</tex-math></inline-formula>. In this paper, we aim to construct quantum codes from skew constacyclic codes over <inline-formula><tex-math id=\"M10\">begin{document}$ R_{ell,m} $end{document}</tex-math></inline-formula>. First, we discuss the structures of skew constacyclic codes and determine their Euclidean dual codes. Then a relation between these codes and their Euclidean duals has been obtained. Finally, with the help of a duality-preserving Gray map and the CSS construction, many MDS and better non-binary quantum codes are obtained as compared to the best-known quantum codes available in the literature.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"116 1","pages":"900-919"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90554973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 12

Nonexistence of some ternary linear codes with minimum weight -2 modulo 9 若干最小权值为-2模9的三元线性码的不存在性

IF 0.9 4区计算机科学

Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2021052

Toshiharu Sawashima, T. Maruta

{"title":"Nonexistence of some ternary linear codes with minimum weight -2 modulo 9","authors":"Toshiharu Sawashima, T. Maruta","doi":"10.3934/amc.2021052","DOIUrl":"https://doi.org/10.3934/amc.2021052","url":null,"abstract":"One of the fundamental problems in coding theory is to find <inline-formula><tex-math id=\"M3\">begin{document}$ n_q(k,d) $end{document}</tex-math></inline-formula>, the minimum length <inline-formula><tex-math id=\"M4\">begin{document}$ n $end{document}</tex-math></inline-formula> for which a linear code of length <inline-formula><tex-math id=\"M5\">begin{document}$ n $end{document}</tex-math></inline-formula>, dimension <inline-formula><tex-math id=\"M6\">begin{document}$ k $end{document}</tex-math></inline-formula>, and the minimum weight <inline-formula><tex-math id=\"M7\">begin{document}$ d $end{document}</tex-math></inline-formula> over the field of order <inline-formula><tex-math id=\"M8\">begin{document}$ q $end{document}</tex-math></inline-formula> exists. The problem of determining the values of <inline-formula><tex-math id=\"M9\">begin{document}$ n_q(k,d) $end{document}</tex-math></inline-formula> is known as the optimal linear codes problem. Using the geometric methods through projective geometry and a new extension theorem given by Kanda (2020), we determine <inline-formula><tex-math id=\"M10\">begin{document}$ n_3(6,d) $end{document}</tex-math></inline-formula> for some values of <inline-formula><tex-math id=\"M11\">begin{document}$ d $end{document}</tex-math></inline-formula> by proving the nonexistence of linear codes with certain parameters.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"77 1","pages":"1338-1357"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90358202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Classical reduction of gap SVP to LWE: A concrete security analysis

IF 0.9 4区计算机科学

Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/AMC.2021004

P. Sarkar, Subhadip Singha

引用次数: 2

Various structures of cyclic codes over the non-Frobenius ring $mathbb{F}_p[u, v] /leftlangle u^2, v^2, u v, v urightrangle$ 非frobenius环上循环码的各种结构$mathbb{F}_p[u, v] /leftlangle u^2, v^2, u v, v urightrangle$

IF 0.9 4区计算机科学

Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023030

H. Choi, Boran Kim

引用次数: 0

PMNS for cryptography: A guided tour 密码学的PMNS:导览

4区计算机科学

Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023033

Nicolas Méloni, François Palma, Pascal Véron

引用次数: 0

Constructions of mismatched binary periodic complementary pairs 错配二进制周期互补对的构造

IF 0.9 4区计算机科学

Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023006

Lina Shi, Ruibin Ren, Yang Yang

引用次数: 0

A new class of optimal wide-gap one-coincidence frequency-hopping sequence sets 一类新的最优宽间隙单符合跳频序列集

IF 0.9 4区计算机科学

Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/AMC.2020131

Wenli Ren, Feng Wang

引用次数: 2

Constacyclic and quasi-twisted codes over $ mathbb{Z}_{q}[u]/langle u^{2}-1rangle $ and new $ mathbb{Z}_4 $-linear codes $ mathbb{Z}_{q}[u]/langle u^{2}-1rangle $上的恒环和拟扭曲码及新的$ mathbb{Z}_4 $-线性码

IF 0.9 4区计算机科学

Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023026

Amina Bellil, K. Guenda, N. Aydin, Peihan Liu, T. Aaron Gulliver

引用次数: 0

On some codes from rank 3 primitive actions of the simple Chevalley group $ G_2(q) $ 关于简单Chevalley群$ G_2(q) $ 3阶基元作用的一些码

IF 0.9 4区计算机科学

Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2022016

Tung Le, B. Rodrigues

{"title":"On some codes from rank 3 primitive actions of the simple Chevalley group $ G_2(q) $","authors":"Tung Le, B. Rodrigues","doi":"10.3934/amc.2022016","DOIUrl":"https://doi.org/10.3934/amc.2022016","url":null,"abstract":"Let <inline-formula><tex-math id=\"M2\">begin{document}$ G_2(q) $end{document}</tex-math></inline-formula> be a Chevalley group of type <inline-formula><tex-math id=\"M3\">begin{document}$ G_2 $end{document}</tex-math></inline-formula> over a finite field <inline-formula><tex-math id=\"M4\">begin{document}$ mathbb{F}_q $end{document}</tex-math></inline-formula>. Considering the <inline-formula><tex-math id=\"M5\">begin{document}$ G_2(q) $end{document}</tex-math></inline-formula>-primitive action of rank <inline-formula><tex-math id=\"M6\">begin{document}$ 3 $end{document}</tex-math></inline-formula> on the set of <inline-formula><tex-math id=\"M7\">begin{document}$ frac{q^3(q^3-1)}{2} $end{document}</tex-math></inline-formula> hyperplanes of type <inline-formula><tex-math id=\"M8\">begin{document}$ O_{6}^{-}(q) $end{document}</tex-math></inline-formula> in the <inline-formula><tex-math id=\"M9\">begin{document}$ 7 $end{document}</tex-math></inline-formula>-dimensional orthogonal space <inline-formula><tex-math id=\"M10\">begin{document}$ {{rm{PG}}}(7, q) $end{document}</tex-math></inline-formula>, we study the designs, codes, and some related geometric structures. We obtained the main parameters of the codes, the full automorphism groups of these structures, and geometric descriptions of the classes of minimum weight codewords.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"52 1","pages":"207-226"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81289202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","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 APN-ness and differential uniformity of some classes of $ (n,n) $-functions over $ mathbb{F}_2^n $ $ mathbb{F}_2^n $上$ (n,n) $-函数的apn -性和微分均匀性

IF 0.9 4区计算机科学

Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023027

C. Carlet

引用次数: 0