Abstract
Recently there has been a lot of interest on algebraic codes in the setting of skew polynomial rings. In this paper we have studied skew quasi-cyclic (QC) codes over Galois rings. We have given a necessary and sufficient condition for skew cyclic codes over Galois rings to be free, and determined a distance bound for free skew cyclic codes. A sufficient condition for 1-generator skew QC codes to be free is determined. Some distance bounds for free 1-generator skew QC codes are discussed. A canonical decomposition of skew QC codes is presented.
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Communicated by J. D. Key.
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Bhaintwal, M. Skew quasi-cyclic codes over Galois rings. Des. Codes Cryptogr. 62, 85–101 (2012). https://doi.org/10.1007/s10623-011-9494-0
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DOI: https://doi.org/10.1007/s10623-011-9494-0