Self-Conjugate-Reciprocal Irreducible Monic Polynomials over Finite Fields
Arunwan Boripan, Somphong Jitman, Patanee Udomkavanich
TL;DR
This paper investigates SCRIM polynomials over finite fields, providing conditions for their irreducibility and formulas for counting their number based on degree.
Contribution
It offers necessary and sufficient conditions for SCRIM polynomials to be irreducible and determines their quantity for any given degree.
Findings
Conditions for monic irreducible SCRIM polynomials are established.
Formulas for counting SCRIM polynomials of a given degree are derived.
Theoretical framework enhances understanding of polynomial structures over finite fields.
Abstract
The class of self-conjugate-reciprocal irreducible monic (SCRIM) polynomials over finite fields are studied. Necessary and sufficient conditions for monic irreducible polynomials to be SCRIM are given. The number of SCRIM polynomials of a given degree are also determined.
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 · Cellular Automata and Applications · Islamic Finance and Communication