Expression for primitive idempotents of length 8pn and corresponding codes

Abstract

The group algebra FG of the group G of order 8pⁿ over the field F of prime power order q, where p is an odd prime n≥1, q is of the form 8k+1 and q is primitive root modulo pⁿ, have 8(n+1) primitive idempotents. The explicit expressions for these idempotents are obtained. Generating polynomials, minimum distances and dimensions for the corresponding minimal cyclic codes are also obtained.