Decoding some doubly-even self-dual [32, 16, 8] codes by hand
Jon-Lark Kim, Vera S. Pless · 2002
. The purpose of this paper is to decode some binary doubly-even self-dual [32; 16; 8] codes by hand. We will decode C84(or 8f4 ) in detail. Our method is the syndrome decoding method used in [G3] to decode the binary Reed-Muller code R(2; 5). At the end we also describe how to decode another doubly-even self-dual [32; 16; 8] code C83(or 2g16 ) and three singly-even selfdual [32; 16; 8] codes by using the syndrome decoding method. 1991 Mathematics Subject Classication: primary 94B35; secondary 94B05. 1. Introduction Our notation follows [MS, P2]. A linear [n; k] code C over GF (2) is a k- dimensional vector subspace of GF (2) n , where GF (2) is the Galois eld with two elements. The weight wt(c) of a codeword c 2 C is the number of nonzero components of c. The minimum nonzero weight d of all codewords in C is called the minimum weight of C. An [n; k; d] code is an [n; k] code with minimum weight d. The dual code C ? of C consists of vectors in GF (2) orthogonal to all vectors ...