Decoding of cyclic codes over F/sub 2/+uF/sub 2/

Abstract

We give a simple decoding algorithm to decode linear cyclic codes of odd length over the ring R=F/sub 2/+uF/sub 2/={0,1,u,u~=u+1}, where u/sup 2/=0. A spectral representation of the cyclic codes over R is given and a BCH-like bound is given for the Lee distance of the codes. The ring R shares many properties of Z/sub 4/ and F/sub 4/ and admits a linear "Gray map".