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.
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The authors are deeply grateful to the editor for his valuable suggestions and comments for improving the presentation of this paper.
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Communicated by Thomas Aaron Gulliver.
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Alimoradi, M.R., Samei, K. Decoding of cyclic codes over the ring \(F_2+uF_2+u^2F_2\). Comp. Appl. Math. 40, 96 (2021). https://doi.org/10.1007/s40314-021-01487-6
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DOI: https://doi.org/10.1007/s40314-021-01487-6