Polynomials with Odd Orthogonal Multiplicity |
| |
Authors: | Alan GB Lauder |
| |
Institution: | Department of Mathematics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, United Kingdomf1 |
| |
Abstract: | Let theorthogonal multiplicityof a monic polynomialgover a field be the number of polynomialsfover , coprime togand of degree less than that ofg, such that all the partial quotients of the continued fraction expansion off/gare of degree 1. Polynomials with positive orthogonal multiplicity arise in stream cipher theory, part of cryptography, as the minimal polynomials of the initial segments of sequences which have perfect linear complexity profiles. This paper focuses on polynomials which have odd orthogonal multiplicity; such polynomials are characterized and a lower bound on their orthogonal multiplicity is given. A special case of a conjecture on rational functions over the finite field of two elements with partial quotients of degree 1 or 2 in their continued fraction expansion is also proved. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|