两类子域码的重量分布

The Weight Distributions of Two Classes of Subfield Codes

子域码是一类特殊的线性码.线性码由于其有效的编码及译码算法,在电子消费产品、数据存储系统和通信系统中有广泛的应用.然而,确定线性码的重量分布通常是困难的工作.本文给出了两类二元子域码C((H(f)<sub>1))(2)和C((H(f)<sub>2))(2)及其对偶码的重量分布,其中f_(1)(x)=x^(4),f_(2)(x)=x^(6)+x^(4)+x^(2).

Subfield codes are a special class of cyclic codes.Cyclic codes have wideapplications in consumer electronics,data storage systems,and communication systems due to their efficient encoding and decoding algorithms.However,the determination of weight distributions is a hard problem in general.In this paper,we determine the weight distributions of two classes of binary subfield codes C((H(f)<sub>1))(2) and C((H(f)<sub>2))(2) and their duals,where f_(1)(x)=x^(4),f_(2)(x)=x^(6)+x^(4)+x^(2).