Application of Fourier Transform over Finite Fields to Error-Correcting Codes,

摘要

BCH code is one of the most powerful and the most extensively studied classes of algebraic error-correcting codes. Unfortunately,it was found that its performance in error-correction deteriorates as its length increases. In this report, a class of algebraic linear codes is proposed,based on the structure of Fourier Transform over finite fields. This class of codes includes the BCH codes,and Srivastava codes as proper subclasses. Several constructive bounds on the minimum distance of these codes are derived and are shown to be achievable using Berlekamp's iterative decoding algorithm,or using Goppa's method based on divided difference. A new distance bound is also obtained for a group of binary Srivastava codes. (Modified author abstract)