Upper Bound on the Number of Full Cycle Codewords of Cyclic Codes

In this paper, we first derive an upper bound on the number of full cycle codewords of a cyclic code. Then we study the numbers of full cycle codewords of two classes of cyclic codes, one is Reed-Solomon code and the other is general cyclic code. For Reed-Solomon code, we get the number of its full cycle codewords. Further, we present a condition under which the Reed-Solomon code has (near) maximum number of full cycle codewords. For general cyclic code, we also get a condition under which it has maximum number of full cycle codewords.