Weight Distributions of Cyclic Codes over Finite Chain Rings
The weight distribution of linear codes is an important research problem in coding theory.Linear codes with a few weights are widely applied in constructing authentication codes,secret sharing schemes with nice access structures,association schemes,constant composition codes and strongly regular graphs.Let R=(F)q+u(F)q be a finite chain ring,where q is an odd prime power,(F)q denotes the finite field with q elements and u2=0.In this paper,we construct a family of cyclic codes over the finite chain ring R,which are obtained from two extension rings of R.By Gauss sums over finite fields,the weight distribution of this class of cyclic codes is investigated.As an application,a class of three-weight linear codes over finite fields which is optimal and minimal is constructed by the Gray map.
Weight distributionsGauss sumsfinite chain ringsoptimal linear codes
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