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.

Udaya和Bonnecaze（IEEE Trans Inf Theory 45：2148-2157，1999）提出了一种在环\（F_2 + u F_2 \）上奇数长度的循环码的解码算法。在这项研究中，提出了一种更简单的方法来解码在该环上具有奇数长度的循环码。环\（R = F_2 + uF_2 + u ^ 2F_2 \）上奇数长度的循环码的结构，其中\（u ^ 3 = 0，\）给出。定义了既是等距图又是从\（R ^ n \）到\（{F_2} ^ {4n} \）的权重保留图的Gray映射，并使用建议的Gray映射（类似于BCH的边界）给出了超过R的代码的Lee距离。最后，针对R上的循环码，提出了一种解码算法。