Decoding of cyclic codes over the ring $$F_2+uF_2+u^2F_2$$

Abstract

Udaya and Bonnecaze (IEEE Trans Inf Theory 45:2148–2157, 1999) presented a decoding algorithm for cyclic codes of odd length over the ring $$F_2+u F_2$$ . In this study, a simpler approach for decoding cyclic codes with odd length over this ring is proposed. The structure of cyclic codes of odd length over the ring $$R=F_2+uF_2+u^2F_2$$ , where $$u^3=0,$$ is given. A Gray map which is both an isometry and a weight-preserving map from $$R^n$$ to $${F_2}^{4n}$$ is defined and with the use of proposed Gray map, a BCH-like bound for the Lee distance of codes over R is given. Finally, a decoding algorithm is suggested for cyclic codes over R.