Three-Weight Ternary Linear Codes from a Family of Monomials
Yongbo Xia, Chunlei Li
TL;DR
This paper introduces two classes of ternary three-weight linear codes derived from power functions, including APN functions, with their weight distributions analyzed through exponential sums.
Contribution
It presents a new generic construction of ternary three-weight linear codes from a family of power functions, expanding the understanding of their weight distributions.
Findings
Two classes of ternary three-weight linear codes are constructed.
Weight distributions are explicitly determined using exponential sums.
Includes codes derived from APN power functions.
Abstract
Based on a generic construction, two classes of ternary three-weight linear codes are obtained from a family of power functions, including some APN power functions. The weight distributions of these linear codes are determined through studying the properties of some exponential sum related to the proposed power functions.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cellular Automata and Applications