Hierarchical Quasi-cyclic Codes: Algebraic Construction and Parameter Bounds
Published:Dec 29, 2025 21:26
•1 min read
•ArXiv
Analysis
This paper introduces a novel algebraic construction of hierarchical quasi-cyclic codes, a type of error-correcting code. The significance lies in providing explicit code parameters and bounds, particularly for codes derived from Reed-Solomon codes. The algebraic approach contrasts with simulation-based methods, offering new insights into code properties and potentially improving minimum distance for binary codes. The hierarchical structure and quasi-cyclic nature are also important for practical applications.
Key Takeaways
- •Introduces the first algebraically constructed hierarchical quasi-cyclic codes.
- •Codes are built from Reed-Solomon codes using a 1964 construction.
- •Provides explicit code parameters and bounds on rank and distance.
- •Some codes meet the best known minimum distance for binary codes.
- •Presents a novel algebraic approach, contrasting with simulation-based methods.
Reference
“The paper provides explicit code parameters and properties as well as some additional bounds on parameters such as rank and distance.”