论文标题
关于有限场上多项式的因素化的数量
On the Number of Factorizations of Polynomials over Finite Fields
论文作者
论文摘要
通过编码应用的激励，考虑了两个枚举问题：f = gf（q）的多项式多项式的独特分隔次数，并且可以将多项式写入f的两个多项式的乘积。对于两个多项式的n多项式。对于两个问题，在两个问题上，最大程度地提出了一个范围，以最大程度地构成多个因素的范围。最后，对于任何给定的M（分别为n），为因素化数量的平均值和因数的差异提供了表达式。
Motivated by coding applications,two enumeration problems are considered: the number of distinct divisors of a degree-m polynomial over F = GF(q), and the number of ways a polynomial can be written as a product of two polynomials of degree at most n over F. For the two problems, bounds are obtained on the maximum number of factorizations, and a characterization is presented for polynomials attaining that maximum. Finally, expressions are presented for the average and the variance of the number of factorizations, for any given m (respectively, n).
