Decoding of cyclic codes over the ring \(F_2+uF_2+u^2F_2\). (English) Zbl 1476.94054
Summary: P. Udaya and A. Bonnecaze [IEEE Trans. Inf. Theory 45, No. 6, 2148–2157 (1999; Zbl 0959.94028)] 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 \(R\).
Citations:
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