Coding Theory pp 42-60

# Cyclic Codes

• Jacobus H. van Lint
Part of the Lecture Notes in Mathematics book series (LNM, volume 201)

## Abstract

Ir. this chapter R(n) will denote the n-dimensional vector space over GF(q). We shall make the restriction (n,q) = 1. Consider the ring R of all polynomials with coefficients in GF(q), i.e. (GF(q)[x],+,). Let S be the principal ideal in R generated by the polynomial xn − 1, i.e. S := (({xn−1}),+,). R/S is the residue class ring R mod S, i.e. (GF(q)[x] mod ({xn−1},+,). The elements of this ring can be represented by polynomials of degree < n with coefficients in GF(q). The additive group of R/S is isomorphic to R(n). An isomorphism is given by associating the vector a = (a0,a1,...,an−1) with the polynomial a0 + a1x + ... + an−1xn−1.

## Keywords

Code Word Cyclic Code Minimal Polynomial Principal Ideal Primitive Element
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.