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).

翻译：以编码应用程序为动力,考虑了两个查点问题:F=GF(q)以上度-多元度-多元度-多元度-不同差数数和多数值-多数值-多数值-多数值-最多为n-F的产物。 对于这两个问题,根据最大乘数乘以乘数,得出界限,对达到这一上限的多数值-多数值-进行定性。最后,对平均值和因数-因数-的差别,对任一特定米(分别是n、n)作了表述。