This benefit becomes more
useful as the number of fingers supported in the RAKE receiver increases.
7.5 PN CODE PROPERTIES
In this section, we will begin by presenting some properties of PN codes and then discuss the maximal
length sequences, Gold codes, and orthogonal codes. Some preliminary information includes a discussion
on Galois fields (GFs). A field is a set of elements in which we can do addition, subtraction,
multiplication, and division without ever leaving the set. When this field contains a finite number of
elements, it is a finite field, also known as Galois field [10]. Here we list some general statements.
??? GF(2n) means there exists a Galois field of 2n elements.
??? A polynomial with coefficients from a binary field, GF(2), is called a binary polynomial.
??? A binary polynomial p(x) of degree m is said to be irreducible if it is not divisible by any binary
polynomial of degrees less than m and greater than 0.
??? An irreducible polynomial p(x) of degree m is said to be a primitive if the smallest positive integer
n for which p(x) divides xn 1 is n 2m 1. For example, p(x) 1 x x4 is a primitive polynomial
because the smallest integer for which 1 x x4 divides xn 1 is n 24 1 15.
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