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

Nial 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1971

Authors and Affiliations

  • Jacobus H. van Lint
    • 1
  1. 1.California Institute of TechnologyPasadenaUSA

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