Sequences of binary irreducible polynomials
Simone Ugolini

TL;DR
This paper presents a method to generate an infinite sequence of binary irreducible polynomials starting from any initial irreducible polynomial, with degrees doubling after a finite initial segment, useful for applications in coding theory and cryptography.
Contribution
The paper introduces a novel construction for infinite binary irreducible polynomial sequences with predictable degree growth, starting from any initial irreducible polynomial.
Findings
Sequence of polynomials becomes degree-doubling after finite steps
Construction works for any initial irreducible polynomial over
Finite initial segment length depends on the degree of the starting polynomial
Abstract
In this paper we construct an infinite sequence of binary irreducible polynomials starting from any irreducible polynomial . If is of degree , where is odd and is a non-negative integer, after an initial finite sequence of polynomials with , the degree of is twice the degree of for any .
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.
