Cyclic Codes of Length 2𝑚

Proceedings Mathematical Sciences

Manju Pruthi¹ 

[1] Department of Mathematics, M.D. University P.G. Regional Centre, Rewari 0, India$$

关键词: Cyclotomic cosets;    generator polynomial;    idempotent generator;    [𝑛;    𝑘;    𝑑] cyclic codes.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper explicit expressions of 𝑚 + 1 idempotents in the ring $R = F_q[X]/langle X^{2^m}-1angle$ are given. Cyclic codes of length 2𝑚 over the finite field 𝐹𝑞, of odd characteristic, are defined in terms of their generator polynomials. The exact minimum distance and the dimension of the codes are obtained.

【 授权许可】

Unknown