Generalized Hamming weights of linear codes (original) (raw)

Error control codes are widely used to increase the reliability of transmission of information over various forms of communications channels. The Hamming weight of a codeword is the number of nonzero entries in the word; the weights of the words in a linear code determine the error-correcting capacity of the code. The r th generalized Hamming weight for a linear code C, denoted by d r (C), is the minimum of the support sizes for r-dimensional subcodes of C. For instance, d 1 (C) equals the traditional minimum Hamming weight of C. In 1991, Feng, Tzeng, and Wei proved that the second generalized Hamming weight d 2 (C) = 8 for all double-error correcting BCH(2 m , 5) codes. We study d 3 (C) and higher Hamming weights for BCH(2 m , 5) codes by a close examination of the words of weight 5. end: