Primitive Idempotents in R8pn and Corresponding Codes

Abstract

Let F be a finite field of prime power order q, where q is of the form 8k + 3 . If q is primitive root modulo pn, then the semi-simple group algebra FG of the cyclic group G of order 8pn over F , where p is an odd prime and n ≥ 1, has 8n + 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.