Generalized Fourier Transform Pair Codes

This letter is concerned with Fourier transform pair (FTP) codes over finite fields. Given any element of order n in a finite field, we can construct an FTP code with length $2n$ , dimension n, and minimum distance at least $2\sqrt {n}$ . Distinguishingly, an FTP code defined with any element (if it exists) of order 2, 3 or 5 in a finite field is a maximum distance separable code. In this letter, we extend the FTP codes to generalized FTP (GFTP) codes. To show the superiority of the GFTP codes over the FTP codes, we compute the binary weight spectra of the GFTP codes, approaching more close than the FTP codes to that of the random codes. We also apply the ordered statistic decoding with local constraints (LC-OSD) algorithm to the binary image of GFTP codes. Numerical results show that the GFTP codes perform better than the FTP codes as the code length increases. Numerical results also show that GFTP codes are comparable with existing codes of the same code rate and similar code length.