Performance of generalized TCH codes for Rayleigh channels

TCH codes are a class of binary nonlinear cyclic codes that have been used in several systems (e.g. mobile satellite, Ultra-Wideband) for tasks like coding and synchronization. The original generating method of this class of codes restricts the length (or period) of the codewords to the set {2, 4, 16, 256, 65536}. In this paper we use an alternative generation method based on the algebraic properties of Zech logarithms that allow us to generalize the construction in a systematic manner and improving the codeword length choices, code size and minimum distance. The performance of these generalized codewords are then evaluated using both AWGN and Rayleigh communication channels and qualitatively compared with the originally extended TCH codewords.