A Decomposition Theory for Binary Linear Codes

New Binary Linear Codes

Binary Linear Block Codes

Coset Decomposition Method for Decoding Linear Codes

We introduced an application of the decomposition of a group into cosets of a subgroup to the theory of error detecting and correcting codes. The proposed approach is based on the general method for decoding linear codes known as syndrome decoding. Mathematics Subject Classification: 20A05; 20B05; 20B40

The Weight Equations for Binary Linear Codes ∗

The system of weight equations for a binary (n,m)-code with respect to its ordered basis is introduced. It connects certain quantities (characteristics) related to the basis with the weights of non-zero words in the code. It is shown that the portion involving the variables does not depend neither on the code nor on the basis. Explicit forms of the matrix of coefficients in the system and its i...

Voronoi regions for binary linear block codes

The Voronoi regions of a block code govern many aspects of the code’s performance on a Gaussian channel, and they are fundamental instruments in, for example, error probability analysis and soft decision decoding. This paper presents an efficient method to find the boundaries of the Voronoi regions for an arbitrary binary linear block code. Two theoretical results together lead to the Voronoi r...