Abstract
In this chapter we give a brief overview of some basic properties of codes over Galois rings. In particular, we focus on the case of codes over GR(pn,1) = \( {Z_p}n \), which are presently an evolving research topic for several applications. Moreover, we shall discuss in more details codes over Z4 by describing their relationship with binary codes. In this case, a fundamental tool of our analysis is the so called Gray map, which will be used to carry out a Z4-interpretation of the formal duality between binary Kerdock codes and some “ad hoc” generalizations of the classical Preparata codes.
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© 2002 Springer Science+Business Media New York
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Bini, G., Flamini, F. (2002). Basic Notions on Codes Over Galois Rings. In: Finite Commutative Rings and Their Applications. The Springer International Series in Engineering and Computer Science, vol 680. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0957-8_8
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DOI: https://doi.org/10.1007/978-1-4615-0957-8_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5323-2
Online ISBN: 978-1-4615-0957-8
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