Some Cyclic Codes of length 8pn, where p is of the form 8k +1 and 8k+5

Explicit formulas for the primitive idempotents in the semisimple group algebra FG, where G is a cyclic group of order 8pn (with q a prime congruent to 1 or 5 (mod 8)), over a finite field F of order q, where q is a primitive root modulo pn. Furthermore, we explicitly determine the generating polynomials, minimum distances, and dimensions of the minimal cyclic codes of length 8pn associated with these idempotents