Good codes from twisted group algebras
Samir Assuena
TL;DR
This paper explores the algebraic structure of constacyclic codes over finite rings and fields using twisted group algebras, providing explicit constructions, isometry characterizations, and new LCD code examples.
Contribution
It offers an explicit proof linking constacyclic codes to ideals in twisted group rings and characterizes LCD codes via algebraic structures and involutions.
Findings
Constacyclic codes can be realized as ideals in twisted group rings.
Isometries between codes are characterized using algebraic structures.
New good LCD codes are constructed and characterized.
Abstract
In this paper, we shall give an explicit proof that constacyclic codes over finite commutative rings can be realized as ideals in some twisted group rings. Also, we shall study isometries between those codes and, finally, we shall study k-Galois LCD constacyclic codes over finite fields. In particular, we shall characterize constacyclic LCD codes with respect to Euclidean inner product in terms of its idempotent generators and the classical involution using the twisted group algebras structures and find some good LCD codes.
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 · Cooperative Communication and Network Coding · Finite Group Theory Research