Galois LCD Codes over Finite Fields
Xiusheng Liu, Yun Fan, Hualu Liu
TL;DR
This paper investigates Galois LCD codes over finite fields, providing conditions for their existence, characterizations for constacyclic codes, and constructions of Hermitian LCD MDS codes with illustrative examples.
Contribution
It introduces a unified method to study Galois LCD codes, characterizes when constacyclic codes are Galois LCD, and constructs new Hermitian LCD MDS codes.
Findings
Necessary and sufficient conditions for Galois LCD codes.
Characterization of constacyclic Galois LCD codes.
Construction of Hermitian LCD MDS codes.
Abstract
In this paper, we study the complementary dual codes in more general setting (which are called Galois LCD codes) by a uniform method. A necessary and sufficient condition for linear codes to be Galois LCD codes is determined, and constacyclic codes to be Galois LCD codes are characterized. Some illustrative examples which constacyclic codes are Galois LCD MDS codes are provided as well. In particular, we study Hermitian LCD constacyclic codes. Finally, we present a construction of a class of Hermitian LCD codes which are also MDS 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 · Cryptographic Implementations and Security · Error Correcting Code Techniques