Enumerating permutation polynomials over finite fields by degree II

AbstractThis note is a continuation of a paper by the same authors that appeared in 2002 in the same journal. First we extend the method of the previous paper proving an asymptotic formula for the number of permutations for which the associated permutation polynomial has d coefficients in specified fixed positions equal to 0. This also applies to the function Nq,d that counts the number of permutations for which the associated permutation polynomial has degree <q-d-1. Next we adopt a more precise approach to show that the asymptotic formula Nq,d∼q!/qd holds for d⩽αq and α=0.03983

Estimates on the Size of Symbol Weight Codes

The study of codes for powerlines communication has garnered much interest over the past decade. Various types of codes such as permutation codes, frequency permutation arrays, and constant composition codes have been proposed over the years. In this work we study a type of code called the bounded symbol weight codes which was first introduced by Versfeld et al. in 2005, and a related family of codes that we term constant symbol weight codes. We provide new upper and lower bounds on the size of bounded symbol weight and constant symbol weight codes. We also give direct and recursive constructions of codes for certain parameters.Comment: 14 pages, 4 figure

Enumerating permutation polynomials over finite fields by degree. II

This note is a continuation of a paper by the same authors that appeared in 2002 in the same journal. First we extend the method of the previous paper proving an asymptotic formula for the number of permutations for which the associated permutation polynomial has d coefficients in specified fixed positions equal to 0. This also applies to the function Nq,d that counts the number of permutations for which the associated permutation polynomial has degree <q-d-1. Next we adopt a more precise approach to show that the asymptotic formula Nq,d∼q!/qd holds for d⩽αq and α=0.03983

Enumerating Permutation Polynomials Over Finite Fields By Degree Ii

This note is an appendix to a paper by the same authors that appeared in 2002 in the same journal. First we extend the method of the result of the previous paper proving an asymptotic formula for the number of permutations for which the associated permutation polynomial has d coe#cients in specified fixed positions equal to 0. This also applies to the function N q,d that counts the number of permutation for which the associated permutation polynomial has degree &lt; q -d-1