✦ LIBER ✦

Orthogonal Sequences of Polynomials over Arbitrary Fields

✍ Scribed by Simon R. Blackburn

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 325 KB
Volume: 68
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1997.2201

No coin nor oath required. For personal study only.

✦ Synopsis

Let f and g be polynomials over some field, thought of as elements of the ring of one-sided Laurent series, and suppose that deg f<deg g. The quotient fÂg is badly approximable if all the partial quotients of the continued fraction expansion of fÂg have degree 1. We investigate the set of polynomials which occur as the denominators g of badly approximable quotients fÂg. Such polynomials arise in stream cipher theory (part of cryptography) as the minimal polynomials of sequences with perfect linear complexity profile. They also occur in the theory of linear cellular automata and in the analysis of certain pseudorandom number generators.

📜 SIMILAR VOLUMES

Factorization of Polynomials over Finite

Factorization of Polynomials over Finite Fields and Characteristic Sequences

✍ Harald Niederreiter; Rainer Göttfert 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 360 KB

Polynomial Distribution and Sequences of

Polynomial Distribution and Sequences of Irreducible Polynomials over Finite Fields

✍ Wun-Seng Chou; Stephen D Cohen 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 153 KB

Let k=GF(q) be the finite field of order q. Let f 1 (x), f 2 (x) # k[x] be monic relatively prime polynomials satisfying n=deg f 1 >deg f 2 0 and f 1 (x)Âf 2 (x){ g 1 (x p )Âg 2 (x p ) for any g 1 (x), g 2 (x) # k[x]. Write Q(x)= f 1 (x)+tf 2 (x) and let K be the splitting field of Q(x) over k(t). L

Derivations and Radicals of Polynomial I

Derivations and Radicals of Polynomial Ideals over Fields of Arbitrary Characteristic

✍ E. Fortuna; P. Gianni; B. Trager 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 306 KB

The purpose of this paper is to give a complete effective solution to the problem of computing radicals of polynomial ideals over general fields of arbitrary characteristic. We prove that Seidenberg's "Condition P" is both a necessary and sufficient property of the coefficient field in order to be a

A Class of Polynomials over Finite Field

A Class of Polynomials over Finite Fields

✍ Arnaldo Garcia; Henning Stichtenoth 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 129 KB

Generalizing the norm and trace mappings for % O P /% O , we introduce an interesting class of polynomials over "nite "elds and study their properties. These polynomials are then used to construct curves over "nite "elds with many rational points.

Groups of Permutation Polynomials over F

Groups of Permutation Polynomials over Finite Fields

✍ Richard M. Stafford 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 195 KB

Let F be a finite field. We apply a result of Thierry Berger (1996, Designs Codes Cryptography, 7, 215-221) to determine the structure of all groups of permutations on F generated by the permutations induced by the linear polynomials and any power map which induces a permutation on F.

The Factorization of Dickson Polynomials

The Factorization of Dickson Polynomials over Finite Fields

✍ Wun-Seng Chou 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 257 KB

Let T n (x, a) ʦ GF(q)[x] be a Dickson polynomial over the finite field GF(q) of either the first kind or the second kind of degree n in the indeterminate x and with parameter a. We give a complete description of the factorization of T n (x, a) over GF(q).