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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1971 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
van Lint, J.H. (1971). Cyclic Codes. In: Coding Theory. Lecture Notes in Mathematics, vol 201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-20712-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-662-20712-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-05476-4
Online ISBN: 978-3-662-20712-3
eBook Packages: Springer Book Archive
