MacWilliams type identities on the Lee and Euclidean weights for linear codes over $\mathbb{Z}_{\ell}$
Yongsheng Tang, Shixin Zhu, Xiaoshan Kai
TL;DR
This paper investigates conditions under which MacWilliams type identities hold for Lee and Euclidean weight enumerators of linear codes over ac, providing necessary and sufficient criteria and illustrative examples.
Contribution
It establishes necessary and sufficient conditions for the existence of MacWilliams identities for Lee and Euclidean weights over ac, extending previous work.
Findings
Derived necessary and sufficient conditions for MacWilliams identities
Provided examples illustrating the identities
Extended understanding of weight enumerator relationships
Abstract
Motivated by the works of Shiromoto [3] and Shi et al. [4], we study the existence of MacWilliams type identities with respect to Lee and Euclidean weight enumerators for linear codes over Necessary and sufficient conditions for the existence of MacWilliams type identities with respect to Lee and Euclidean weight enumerators for linear codes over are given. Some examples about such MacWilliams type identities are also presented.
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 · Finite Group Theory Research · graph theory and CDMA systems