2005/01/22 by Salah A. Aly, Salah Aly, Andreas Klappenecker +4
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #BCH code #Block code #Coding theory and cryptography #Combinatorics #Decoding methods #Dimension (graph theory) #Discrete mathematics #Error detection and correction #FOS: Computer and information sciences #FOS: Physical sciences #Hermitian matrix #Information Theory (cs.IT) #Linear code #Mathematics #Pure mathematics #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #cs.IT #math.IT #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0501126
5 pages; title changed, references added, revised
openalex publication_date 2005/01/22 · arxiv created 2006/01/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
An attractive feature of BCH codes is that one can infer valuable information from their design parameters (length, size of the finite field, and designed distance), such as bounds on the minimum distance and dimension of the code. In this paper, it is shown that one can also deduce from the design parameters whether or not a primitive, narrow-sense BCH contains its Euclidean or Hermitian dual code. This information is invaluable in the construction of quantum BCH codes. A new proof is provided for the dimension of BCH codes with small designed distance, and simple bounds on the minimum distance of such codes and their duals are derived as a consequence. These results allow us to derive the parameters of two families of primitive quantum BCH codes as a function of their design parameters.