Linearized Reed-Solomon codes and linearized Wenger graphs
Haode Yan, Chunlei Liu
TL;DR
This paper investigates the properties of linearized Reed-Solomon codes and their associated Wenger graphs, focusing on weight distribution and structural relationships within these algebraic and graph-theoretic frameworks.
Contribution
It introduces new results on the weight distribution of linearized Reed-Solomon codes and connects these findings to properties of Wenger graphs derived from linearized polynomials.
Findings
Determined the weight distribution of codewords in linearized Reed-Solomon codes.
Established a relationship between linearized polynomials and Wenger graphs.
Provided new insights into the structure of Wenger graphs from linearized polynomials.
Abstract
A codeword is associated to a linearized polynomial. The weight distribution of the codewords is determined as the linearized polynomial varies in a family of fixed degree. There is a corresponding result on Wenger graphs from linearized polynomials.
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Taxonomy
TopicsCoding theory and cryptography · Cellular Automata and Applications · graph theory and CDMA systems