On Cyclic Codes with Length 2p^e over Finite Fields  

作　　者：PANG Binbin ZHU Shixin SUN Zhonghua 

机构地区：[1]School of Mathematics,Hefei University of Technology,Hefei 230601,China

出　　处：《Chinese Journal of Electronics》2020年第4期672-677,共6页电子学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.61772168,No.61572168);the Natural Science Foundation of Anhui Province(No.1708085QA01,No.2008085QA04)。

摘　　要：Cyclic codes are an important class of linear codes.Cyclic codes are applied in data storage,communication systems and consumer electronics due to their efficient encoding and decoding algorithms.We utilize the cyclotomy of order 2 to study the cyclic codes with length n=2p^e and dimension k=n/2=p^e.The cyclic codes from our construction are either optimal or almost optimal among all cyclic codes with the same length and dimension.We get the enumeration of these cyclic codes and study the hull of cyclic codes of length n over Fq.We obtain the range of l=dim(Hull(C)).Finally,we construct and enumerate cyclic codes of length n having hull of given dimension.

关 键 词：Cyclic codes CYCLOTOMY HULL Primitive root 

分 类 号：O157.4[理学—数学]