Primitive Idempotents in R8pn and Corresponding Codes

Author : Dr Jagbir Singh

Abstract :Let F be a finite field of prime power order modulo , then the semi-simple group algebra is an odd prime and , has where is of the form . If q is primitive root of the cyclic group of order over , where primitive idempotents. Explicit expressions for these primitive idempotents are obtained. Generating polynomials, minimum distances and dimensions of the corresponding minimal cyclic codes are also obtained.

Keywords :Group algebra, cyclotomic cosets, primitive idempotents, generating polynomials.

Conference Name :International Conference on Mathematical ,Computational Sciences and Management ( ICMACOSCMA-25)

Conference Place Coimbatore, India

Conference Date 21st Sep 2025