Extended‐BCH codes using fourier transform over a finite field
Yoshiyuki Miyabe, Kin‐ichiroh Tokiwa, Masao Kasahara, Toshihiko Namekawa · Electronics and Communications in Japan (Part I Communications) · 1983
Abstract This paper proposes a new construction method of extended codes based on BCH code using a Fourier transform over a finite field. This method applies encoding to a so‐called “tail” which is added for extension and, furthermore, repeats similar encoding to the encoded tail. the constructed codes based on primitive BCH codes generally are excellent in the point of code rate (= number of information symbols/code length) and it is clarified through examples that some of them improve the lower bounds of the maximum code rate. Since the extended codes constructed by this method can generally be considered over an extended field of one degree lower order compared with the shortened codes with the same code length, the number of multiplications needed for syndrome‐calculation in decoding can be reduced to about a fourth. Moreover, it is shown that when the code is constructed by this method, the fast Fourier transform algorithm can be applied to a wider range of code lengths than before in syndrome‐calculation.