检索结果-南通市图书馆

A Class of constacyclic codes over Ring R+vR

在线全文

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2016年第3期29卷 805-813页

作者： HUANG Lei ZHU Shixin School of Mathematics Hefei University of Technology

By constructing a Gray map, a class of constacyclic codes over ring R = R＋ vR is studied. Using cyclic codes and negacyclic codes of length p^s over ring R, the structure of （1 - 2v）-constacyclic codes and dual codes of length p^s over ring R are given, the Gray images of （1 - 2v）-constacyclic codes in a particular case are also studied. It is shown that linear codes of length pS over ring R are （1 -2v）-constacyclic codes if and only if their Gray images are distance-invariant cyclic codes of length 2p^s over ring R.

关键词： constacyclic code cyclic code dual code Gray map.

On the Gray Images of Some constacyclic codes over Fp ＋ uFp ＋ u^2Fp

在线全文

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2016年第3期29卷 842-849页

作者： YU Haifeng ZHU Shixin KAI Xiaoshan Department of Mathematics and Physics Hefei University Hefei 230601 China. School of Mathematics Hefei University of Technology Hefei 230009 China National Mobile Communications Research Laboratory Southeast University Nanjinq 210096 China.

Abstract constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, a new Gray map between codes over Fp ＋ uFp ＋ u^2Fp and codes over Fp is defined, where p is an odd prime. By means of this map, it is shown that the Gray image of a linear （1 ＋ u ＋ u2）-constacyclic code over Fp ＋ uFp ＋ u^2Fp of length n is a repeated-root cyclic code over Fp of length pn. Furthermore, some examples of optimal linear cyclic codes over F3 from （1 ＋ u ＋ u2）-constacyclic codes over F3 ＋ uF3 ＋ u^2F3 are given.

关键词： constacyclic code cyclic code Gray map.

Quantum codes from constacyclic codes over Polynomial Residue Rings

在线全文

学校读者我要写书评

暂无评论

Chinese Journal of Electronics 2019年第6期28卷 1131-1138页

作者： DING Jian LI Hongju LIANG Jing TANG Yongsheng College of Mathematics and Informatics Fujian Normal University Fujian Provincial Key Lab of Network Security and Cryptology Fujian Normal University Department of General Education Anhui Xinhua University School of Mathematics and Statistics Hefei Normal University

Sufficient and necessary conditions for Hermitian（1 + λu）-constacyclic self-orthogonal codes over F;m +uF;m are obtained, where λ is a unit of F;m +uF;*** on this, a new method for the construction of p;ary quantum codes from the obtained Hermitian（1 + λu）-constacyclic self-orthogonal codes over F;m +uF;m is *** an example, [[p;-1, p;-2d + 1, d]];m quantum MDS codes are constructed for 1 ≤ d ≤（p;+ 1）/2 and p ≠ 2, as well as some other quantum codes.

关键词： Quantum code Quantum MDS code constacyclic code Self-orthogonal code

(1-uv)-constacyclic codeS OVER F_p+uF_p+vF_p+uvF_p

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2014年第4期27卷 811-816页

作者： YU Haifeng ZHU Shixin KAI Xiaoshan Department of Mathematics and Physics Hefei University School of Mathematics Hefei University of Technology

constacyclic codes are an important class of linear codes in coding *** optimal linear codes are directly derived from constacyclic *** this paper,(1 — uv)-constacyclic codes over the local ring F_p + uF_p + vF_p + uvF_p are *** is proved that the image of a(1 — uv)-constacyclic code of length n over F_p + uF_p + vF_p + uvF_p under a Gray map is a distance invariant quasi-cyclic code of index p2 and length p^3n over F_*** examples of optimal linear codes over F_p from(1 — uv)-constacyclic codes over F_p + uF_p + vF_p + uvF_p are given.

关键词： constacyclic code cyclic code gray map quasi-cyclic code.

A FAMILY OF constacyclic codeS OVER F_2+μF_2+ vF_2+ uvF_2

在线全文

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2012年第5期25卷 1032-1040页

作者： Xiaoshan KAI Shixin ZHU Liqi WANG School of Mathematics Hefei University of Technology National Mobile Communications Research Laboratory Southeast University

This paper studies （1 ＋ u）-constacyelic codes over the ring F2 ＋ uF2 ＋ vF,2 ＋ uvF2. It is proved that the image of a （1 ＋ u）-constacyclic code of length n over F2 ＋ uF2 ＋ vF2 ＋uvF2 under a Gray map is a distance invariant binary quasi-cyclic code of index 2 and length 4n. A set of generators of such constacyclic codes for an arbitrary length is determined, Some optimal binary codes are obtained directly from （1 ＋ u）-constacyclic codes over F2 ＋ uF2 ＋ vF2 ＋ uvF2.

关键词： constacyclic code generator polynomial Gray distance Gray map.

Optimal p-ary codes from constacyclic codes over a Non-chain Ring R

在线全文

学校读者我要写书评

暂无评论

Chinese Journal of Electronics 2014年第4期23卷 773-777页

作者： SHI Minjia School of Mathematical Sciences of Anhui University

This paper is devoted to the study of constacyclic codes over a non-chain ring R. The generator polynomials of all constacyclic codes over R are characterized and their dual codes are also determined. We also introduce a Gray map. It is proved that the image of a v-constacyclic code of length n over R under the Gray map is a cyclic code of length 2n over a field with p elements,where p is odd prime. Moreover, we obtain a substantial number of optimal p-ary linear(cyclic) codes, in terms of their parameters, via the Gray map.

关键词： Generator polynomial constacyclic code Gray map Dual code

The Depth Distribution of constacyclic codes Over the Ring F_(p)+vF_(p)+v^(2)F_(p)

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Chinese Quarterly Journal of Mathematics 2021年第4期36卷 430-440页

作者： LI Jian-hao WU Hua-zhang School of Mathematical Sciences Anhui UniversityHeifei 230601China.

In this paper,we studied the depth spectrum and the depth distribution of constacyclic codes over the non-chain ring R=F_(p)+vF_(p)+v^(2)F_(p),where v^(3)=*** decomposing the linear codes C over R into the linear codes over the finite field F_(p),three corresponding constacyclic codes C_(1),C_(2),C_(3) over F_(p)were ***,considering the depth spectrum of constacyclic codes over the finite filed F_(p),and the relationship between constacyclic codes C_(1),C_(2),C_(3) and C,the depth spectrum and the depth distribution of constacyclic codes over R were discussed.

关键词： constacyclic code Depth spectrum Depth distribution Non-chain ring

constacyclic and cyclic codes over finite chain rings

在线全文

学校读者我要写书评

暂无评论

The Journal of China Universities of Posts and Telecommunications 2009年第3期16卷 122-125页

作者： QIAN Jian-fa MA Wen-ping National Key Laboratory of ISN Xidian University Xi' an 710071 China

The problem of Gray image of constacyclic code over finite chain ring is studied. A Gray map between codes over a finite chain ring and a finite field is defined. The Gray image of a linear constacyclic code over the finite chain ring is proved to be a distance invariant quasi-cyclic code over the finite field. It is shown that every code over the finite field, which is the Gray image of a cyclic code over the finite chain ring, is equivalent to a quasi-cyclic code.

关键词： constacyclic code Gray map quasi-cyclic code cyclic code