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There are connections between invariant theory and modular forms
since the times of Felix Klein, in the 19th century, connections
between codes and lattices since the 1960's. The aim of the book is
to explore the interplay between codes and modular forms. Here
modular form is understood in a wide sense (Jacobi forms, Siegel
forms, Hilbert forms). Codes comprises not only linear spaces over
finite fields but modules over some commutative rings. The
connection between codes over finite fields and lattices has been
well documented since the 1970s. Due to an avalanche of results on
codes over rings since the 1990's there is a need for an update at
book level.
Codes and Rings: Theory and Practice is a systematic review of
literature that focuses on codes over rings and rings acting on
codes. Since the breakthrough works on quaternary codes in the
1990s, two decades of research have moved the field far beyond its
original periphery. This book fills this gap by consolidating
results scattered in the literature, addressing classical as well
as applied aspects of rings and coding theory. New research covered
by the book encompasses skew cyclic codes, decomposition theory of
quasi-cyclic codes and related codes and duality over Frobenius
rings. Primarily suitable for ring theorists at PhD level engaged
in application research and coding theorists interested in
algebraic foundations, the work is also valuable to computational
scientists and working cryptologists in the area.
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