Abstract
The group algebra FG of the group G of order 8p n 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 p n , 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.
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