This paper is concerned with cyclically permutable codes, which are n-tuples over a q-ary alphabet with the property that all n cyclic shifts of the code words are unique. Such codes are useful in Code Division Multiple Access (CDMA) systems for encoding spreading sequence information on a pilot channel, and are employed in the 3G WCDMA standard for fast acquisition in an asynchronous base station system. In this paper we show how to determine the number of cyclically permutable code words in all possible n-tuples, and also the number of such code words in error correcting cyclic codes such as Reed-Solomon, BCH, and Hamming codes.
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