Primitive Idempotents and Weight Distributions of Irreducible Cyclic Codes of Length 5l^m

Abstract

Abstract

Let be a finite field with q elements such that and gcd  = 1, where  is a prime. In this paper, we give all primitive idempotents in a ring [x] . We give the weight distributions of all irreducible cyclic codes of length over .

Keywords: Primitive Idempotents, Cyclotomic Cosets, Cyclic Codes.

Cite this Article

Sunil Kumar, Manju Pruthi, Rahul. Primitive Idempotents and Weight Distributions of Irreducible Cyclic Codes of Length . Research & Reviews Discrete Mathematical Structures. 2019; 6(2): 49–58p.