On the complete weight enumerators of some linear codes with a few weights
Minglong Qi, Shengwu Xiong, Jingling Yuan, Wenbi Rao, Luo Zhong

TL;DR
This paper determines the complete weight enumerators of certain linear codes with few weights, providing insights into their weight distributions using Legendre symbol sums, which are valuable for various applications.
Contribution
It introduces methods to explicitly compute the complete weight enumerators of specific linear codes with few weights, advancing understanding of their structure.
Findings
Complete weight enumerators derived for selected linear codes.
Hamming weight distributions obtained from these enumerators.
Method involving Legendre symbol sums used for calculations.
Abstract
Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of linear codes are important research topics. In this paper, we consider some classes of linear codes with a few weights and determine the complete weight enumerators from which the corresponding Hamming weight distributions are derived with help of some sums involving Legendre symbol.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Error Correcting Code Techniques
