GENERATORS IDEMPOTENT IN SEMI-SIMPLE RING $FC_{16p^n}$, FOR THE IDEALS CORRESPONDING TO THE MINIMAL CYCLIC CODES OF LENGTH $16p^n$ AND THE CODES

In semi-simple ring $R_{16p^n}\equiv \frac{GF(q)[x]}{<x^{16p^n}-1>}$, where $p$ is prime and $q$ is some prime power (of type $16k+1$), $n$ is a positive integer, subject to order of $q$ modulo $p^n$ is $\frac{\phi(p^n)}{2}$, expression for primitive idempotents are obtained. Generating polynomials, dimensions and minimum distance bounds for the cyclic codes generated by these idempotents are also calculated.