Generating Idempotents of Quartic Residue Codes over the Field

Abstract

The generating polynomials of higher power residue codes over finite fields are difficult to construct. This paper gives explicit expressions of generating idempotents of quartic residue codes over the field $F_4$.The result will enable one to construct the generating polynomials of quartic residue codes over the field $F_4$ by computing the greatest common divisors of these generating idempotents and the polynomial $x^n-1$ with computer software such as Matlab and Maple.