摘要

As far as we know, there is no decoding algorithm of any binary self-dual [40, 20, 8] code except for the syndrome decoding applied to the code directly. This syndrome decoding for a binary self-dual [40, 20, 8] code is not efficient in the sense that it cannot be done by hand due to a large syndrome table. The purpose of this paper is to give two new efficient decoding algorithms for an extremal binary doubly-even self-dual [40, 20, 8] code by hand with the help of a Hermitian self-dual [10, 5, 4] code over GF(4). The main idea of this decoding is to project codewords of onto so that it reduces the complexity of the decoding of . The first algorithm is called the representation decoding algorithm. It is based on the pattern of codewords of . Using certain automorphisms of , we show that only eight types of codewords of can produce all the codewords of . The second algorithm is called the syndrome decoding algorithm based on . It first solves the syndrome equation in and finds a corresponding binary codeword of C-40, 1(D E).

  • 出版日期2017-6