Primitive Idempotent in FC_(8p)~n and Corresponding Codes

摘要

In semi-simple ring R_(8p)~n ≡ (GF(q)[x])/(), where p and q (of type 8k + 1) are distinct odd primes, n is a positive integer and order of q modulo 8p~n is (Φ(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.