Skip to main content

Cyclic codes

  • Chapter
  • 1055 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 201)

Absract

In 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 = (aO,a1, ... ,an-1) with the polynomial aO + a1x + ... + an-1xn-1.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Rights and permissions

Reprints and Permissions

Copyright information

© 1971 Springer-Verlag Berlin · Heidelberg

About this chapter

Cite this chapter

(1971). Cyclic codes. In: Coding Theory. Lecture Notes in Mathematics, vol 201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36657-7_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-36657-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06363-6

  • Online ISBN: 978-3-540-36657-7

  • eBook Packages: Springer Book Archive