A New Method on the Construction of Optimal Codes over Finite Field

DING Jian; LI Hong-ju

doi:10.3969/j.issn.0372-2112.2015.08.029

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A New Method on the Construction of Optimal Codes over Finite Field

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- A New Method on the Construction of Optimal Codes over Finite Field
- Acta Electronica Sinica Vol. 43, Issue 8, Pages: 1662-1667(2015)
- 作者机构：
  
  安徽新华学院公课部,安徽,合肥,230088
- 作者简介：
- 基金信息：
  
  Natural Scientific Program of Department of Education of Anhui Province (No.KJ2013B107);Research Program and Quality Engineering Project of Anhui Xinhua University (No.2014Zr009, No.2013tskcx06, No.2013jgkcx09, No.2014xgg09)
- DOI：10.3969/j.issn.0372-2112.2015.08.029
  CLC： TN911.22
- Published：2015
- 稿件说明：
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DING Jian, LI Hong-ju. A New Method on the Construction of Optimal Codes over Finite Field[J]. Acta Electronica Sinica, 2015, 43(8): 1662-1667.
DOI：

DING Jian, LI Hong-ju. A New Method on the Construction of Optimal Codes over Finite Field[J]. Acta Electronica Sinica, 2015, 43(8): 1662-1667. DOI： 10.3969/j.issn.0372-2112.2015.08.029.

摘要

基于域

上一类特殊的矩阵

定义了环

(

[

]

到

的一个新的Gray映射

其中

=0、

为素数、

为正整数且

－1

.得到了环

(

)上码长为任意长度

的(1+

)常循环码的Gray象是

上长为

的保距线性循环码

并给出了Gray象的生成多项式

构造了

和

上的一些最优线性循环码.

Abstract

Let

(

) denote the polynomial residue ring

[

]

where

－1

and

=0 for some positive prime number

and positive integer j.Based on a kind of matrix over

a new Gray map from

(

) to

is defined.It is proved that the Gray image of a linear (1+

) constacyclic code of an arbitrary length

over

(

) is a distance invariant linear cyclic code of length

N over

.Moreover

the generator polynomial of the Gray image of such a constacyclic code is determined

and some optimal linear cyclic codes over

and

are constructed via the Gray map.

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LCD Cyclic Codes over ℤ₄ and Binary Images

MacWilliams Identities of Linear Codes Over Ring R+vR+v²R

MacWilliams Identities of Linear Codes over Non-principal ideal Ring F_-p+vF_-p

MacWilliams Identities of Linear Codes Over Ring Z₄ with Respect to the RT Metric

Related Author

LIAO Wen-jing

KAI Xiao-shan

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ZHU Shi-xin

WU Bo

HUANG Lei

ZHU Shi-xin

YANG Shan-lin

Related Institution

School of Mathematics， Hefei University of Technology

School of Mathematics and Computational Science,Anhui University

Department of Matheatics,Hefei University of Technology

School of Mathematics and Computational ScienceAnhui UniversityHefeiAnhui 230039China

Department of MatheaticsHefei University of TechnologyHefeiAnhui 230009China

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