Explicit Expression for Primitive Idempotents of Some Cyclic Codes and Codes Corresponding

Author : Dr Jagbir Singh

Abstract :pn, then the semi-simple group algebra FG of the cyclic group G of order 8 pn over F, where p is an odd prime and n1, has 8 n+ 5 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. AMS Mathematical Subject Classification (2000): 11T71, 11G25, 22D20.

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

Conference Name :International Conference on Informatics and Mathematical Sciences (ICIMS-25)

Conference Place Darjeeling, India

Conference Date 28th Sep 2025